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sphere913/BigInt.cpp

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Created September 7, 2018 09:47
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Revisions

  1. @ar-pa ar-pa revised this gist May 8, 2017. 1 changed file with 21 additions and 2 deletions.
    23 changes: 21 additions & 2 deletions BigInt.cpp
    View file
    Original file line number Diff line number Diff line change
    @@ -58,7 +58,7 @@ struct bigint {

    void operator=(long long v) {
    sign = 1;
    a.clear()
    a.clear();
    if (v < 0)
    sign = -1, v = -v;
    for (; v > 0; v = v / base)
    @@ -120,6 +120,26 @@ struct bigint {
    return res;
    }

    void operator*=(long long v) {
    if (v < 0)
    sign = -sign, v = -v;
    for (int i = 0, carry = 0; i < (int) a.size() || carry; ++i) {
    if (i == (int) a.size())
    a.push_back(0);
    long long cur = a[i] * (long long) v + carry;
    carry = (int) (cur / base);
    a[i] = (int) (cur % base);
    //asm("divl %%ecx" : "=a"(carry), "=d"(a[i]) : "A"(cur), "c"(base));
    }
    trim();
    }

    bigint operator*(long long v) const {
    bigint res = *this;
    res *= v;
    return res;
    }

    friend pair<bigint, bigint> divmod(const bigint &a1, const bigint &b1) {
    int norm = base / (b1.a.back() + 1);
    bigint a = a1.abs() * norm;
    @@ -383,4 +403,3 @@ struct bigint {
    ####################### THE BIG INT ##########################
    ######################################################################
    */

  2. @ar-pa ar-pa revised this gist Feb 21, 2017. 1 changed file with 1 addition and 0 deletions.
    1 change: 1 addition & 0 deletions BigInt.cpp
    View file
    Original file line number Diff line number Diff line change
    @@ -383,3 +383,4 @@ struct bigint {
    ####################### THE BIG INT ##########################
    ######################################################################
    */

  3. @ar-pa ar-pa revised this gist Sep 12, 2016. 1 changed file with 1 addition and 0 deletions.
    1 change: 1 addition & 0 deletions BigInt.cpp
    View file
    Original file line number Diff line number Diff line change
    @@ -58,6 +58,7 @@ struct bigint {

    void operator=(long long v) {
    sign = 1;
    a.clear()
    if (v < 0)
    sign = -1, v = -v;
    for (; v > 0; v = v / base)
  4. @ar-pa ar-pa revised this gist May 15, 2016. 1 changed file with 377 additions and 356 deletions.
    733 changes: 377 additions & 356 deletions BigInt.cpp
    View file
    Original file line number Diff line number Diff line change
    @@ -1,363 +1,384 @@
    /*
    ######################################################################
    ####################### THE BIG INT ##########################
    */
    const int base = 1000000000;
    const int base_digits = 9;
    struct bigint {
    vector<int> a;
    int sign;
    /*<arpa>*/
    int size(){
    if(a.empty())return 0;
    int ans=(a.size()-1)*base_digits;
    int ca=a.back();
    while(ca)
    ans++,ca/=10;
    return ans;
    }
    bigint operator ^(const bigint &v){
    bigint ans=1,a=*this,b=v;
    while(!b.isZero()){
    if(b%2)
    ans*=a;
    a*=a,b/=2;
    }
    return ans;
    }
    /*</arpa>*/
    bigint() :
    sign(1) {
    }

    bigint(long long v) {
    *this = v;
    }

    bigint(const string &s) {
    read(s);
    }

    void operator=(const bigint &v) {
    sign = v.sign;
    a = v.a;
    }

    void operator=(long long v) {
    sign = 1;
    if (v < 0)
    sign = -1, v = -v;
    for (; v > 0; v = v / base)
    a.push_back(v % base);
    }

    bigint operator+(const bigint &v) const {
    if (sign == v.sign) {
    bigint res = v;

    for (int i = 0, carry = 0; i < (int) max(a.size(), v.a.size()) || carry; ++i) {
    if (i == (int) res.a.size())
    res.a.push_back(0);
    res.a[i] += carry + (i < (int) a.size() ? a[i] : 0);
    carry = res.a[i] >= base;
    if (carry)
    res.a[i] -= base;
    }
    return res;
    }
    return *this - (-v);
    }

    bigint operator-(const bigint &v) const {
    if (sign == v.sign) {
    if (abs() >= v.abs()) {
    vector<int> a;
    int sign;
    /*<arpa>*/
    int size(){
    if(a.empty())return 0;
    int ans=(a.size()-1)*base_digits;
    int ca=a.back();
    while(ca)
    ans++,ca/=10;
    return ans;
    }
    bigint operator ^(const bigint &v){
    bigint ans=1,a=*this,b=v;
    while(!b.isZero()){
    if(b%2)
    ans*=a;
    a*=a,b/=2;
    }
    return ans;
    }
    string to_string(){
    stringstream ss;
    ss << *this;
    string s;
    ss >> s;
    return s;
    }
    int sumof(){
    string s = to_string();
    int ans = 0;
    for(auto c : s) ans += c - '0';
    return ans;
    }
    /*</arpa>*/
    bigint() :
    sign(1) {
    }

    bigint(long long v) {
    *this = v;
    }

    bigint(const string &s) {
    read(s);
    }

    void operator=(const bigint &v) {
    sign = v.sign;
    a = v.a;
    }

    void operator=(long long v) {
    sign = 1;
    if (v < 0)
    sign = -1, v = -v;
    for (; v > 0; v = v / base)
    a.push_back(v % base);
    }

    bigint operator+(const bigint &v) const {
    if (sign == v.sign) {
    bigint res = v;

    for (int i = 0, carry = 0; i < (int) max(a.size(), v.a.size()) || carry; ++i) {
    if (i == (int) res.a.size())
    res.a.push_back(0);
    res.a[i] += carry + (i < (int) a.size() ? a[i] : 0);
    carry = res.a[i] >= base;
    if (carry)
    res.a[i] -= base;
    }
    return res;
    }
    return *this - (-v);
    }

    bigint operator-(const bigint &v) const {
    if (sign == v.sign) {
    if (abs() >= v.abs()) {
    bigint res = *this;
    for (int i = 0, carry = 0; i < (int) v.a.size() || carry; ++i) {
    res.a[i] -= carry + (i < (int) v.a.size() ? v.a[i] : 0);
    carry = res.a[i] < 0;
    if (carry)
    res.a[i] += base;
    }
    res.trim();
    return res;
    }
    return -(v - *this);
    }
    return *this + (-v);
    }

    void operator*=(int v) {
    if (v < 0)
    sign = -sign, v = -v;
    for (int i = 0, carry = 0; i < (int) a.size() || carry; ++i) {
    if (i == (int) a.size())
    a.push_back(0);
    long long cur = a[i] * (long long) v + carry;
    carry = (int) (cur / base);
    a[i] = (int) (cur % base);
    //asm("divl %%ecx" : "=a"(carry), "=d"(a[i]) : "A"(cur), "c"(base));
    }
    trim();
    }

    bigint operator*(int v) const {
    bigint res = *this;
    for (int i = 0, carry = 0; i < (int) v.a.size() || carry; ++i) {
    res.a[i] -= carry + (i < (int) v.a.size() ? v.a[i] : 0);
    carry = res.a[i] < 0;
    if (carry)
    res.a[i] += base;
    res *= v;
    return res;
    }

    friend pair<bigint, bigint> divmod(const bigint &a1, const bigint &b1) {
    int norm = base / (b1.a.back() + 1);
    bigint a = a1.abs() * norm;
    bigint b = b1.abs() * norm;
    bigint q, r;
    q.a.resize(a.a.size());

    for (int i = a.a.size() - 1; i >= 0; i--) {
    r *= base;
    r += a.a[i];
    int s1 = r.a.size() <= b.a.size() ? 0 : r.a[b.a.size()];
    int s2 = r.a.size() <= b.a.size() - 1 ? 0 : r.a[b.a.size() - 1];
    int d = ((long long) base * s1 + s2) / b.a.back();
    r -= b * d;
    while (r < 0)
    r += b, --d;
    q.a[i] = d;
    }

    q.sign = a1.sign * b1.sign;
    r.sign = a1.sign;
    q.trim();
    r.trim();
    return make_pair(q, r / norm);
    }

    bigint operator/(const bigint &v) const {
    return divmod(*this, v).first;
    }

    bigint operator%(const bigint &v) const {
    return divmod(*this, v).second;
    }

    void operator/=(int v) {
    if (v < 0)
    sign = -sign, v = -v;
    for (int i = (int) a.size() - 1, rem = 0; i >= 0; --i) {
    long long cur = a[i] + rem * (long long) base;
    a[i] = (int) (cur / v);
    rem = (int) (cur % v);
    }
    trim();
    }

    bigint operator/(int v) const {
    bigint res = *this;
    res /= v;
    return res;
    }

    int operator%(int v) const {
    if (v < 0)
    v = -v;
    int m = 0;
    for (int i = a.size() - 1; i >= 0; --i)
    m = (a[i] + m * (long long) base) % v;
    return m * sign;
    }

    void operator+=(const bigint &v) {
    *this = *this + v;
    }
    void operator-=(const bigint &v) {
    *this = *this - v;
    }
    void operator*=(const bigint &v) {
    *this = *this * v;
    }
    void operator/=(const bigint &v) {
    *this = *this / v;
    }

    bool operator<(const bigint &v) const {
    if (sign != v.sign)
    return sign < v.sign;
    if (a.size() != v.a.size())
    return a.size() * sign < v.a.size() * v.sign;
    for (int i = a.size() - 1; i >= 0; i--)
    if (a[i] != v.a[i])
    return a[i] * sign < v.a[i] * sign;
    return false;
    }

    bool operator>(const bigint &v) const {
    return v < *this;
    }
    bool operator<=(const bigint &v) const {
    return !(v < *this);
    }
    bool operator>=(const bigint &v) const {
    return !(*this < v);
    }
    bool operator==(const bigint &v) const {
    return !(*this < v) && !(v < *this);
    }
    bool operator!=(const bigint &v) const {
    return *this < v || v < *this;
    }

    void trim() {
    while (!a.empty() && !a.back())
    a.pop_back();
    if (a.empty())
    sign = 1;
    }

    bool isZero() const {
    return a.empty() || (a.size() == 1 && !a[0]);
    }

    bigint operator-() const {
    bigint res = *this;
    res.sign = -sign;
    return res;
    }

    bigint abs() const {
    bigint res = *this;
    res.sign *= res.sign;
    return res;
    }

    long long longValue() const {
    long long res = 0;
    for (int i = a.size() - 1; i >= 0; i--)
    res = res * base + a[i];
    return res * sign;
    }

    friend bigint gcd(const bigint &a, const bigint &b) {
    return b.isZero() ? a : gcd(b, a % b);
    }
    friend bigint lcm(const bigint &a, const bigint &b) {
    return a / gcd(a, b) * b;
    }

    void read(const string &s) {
    sign = 1;
    a.clear();
    int pos = 0;
    while (pos < (int) s.size() && (s[pos] == '-' || s[pos] == '+')) {
    if (s[pos] == '-')
    sign = -sign;
    ++pos;
    }
    for (int i = s.size() - 1; i >= pos; i -= base_digits) {
    int x = 0;
    for (int j = max(pos, i - base_digits + 1); j <= i; j++)
    x = x * 10 + s[j] - '0';
    a.push_back(x);
    }
    trim();
    }

    friend istream& operator>>(istream &stream, bigint &v) {
    string s;
    stream >> s;
    v.read(s);
    return stream;
    }

    friend ostream& operator<<(ostream &stream, const bigint &v) {
    if (v.sign == -1)
    stream << '-';
    stream << (v.a.empty() ? 0 : v.a.back());
    for (int i = (int) v.a.size() - 2; i >= 0; --i)
    stream << setw(base_digits) << setfill('0') << v.a[i];
    return stream;
    }

    static vector<int> convert_base(const vector<int> &a, int old_digits, int new_digits) {
    vector<long long> p(max(old_digits, new_digits) + 1);
    p[0] = 1;
    for (int i = 1; i < (int) p.size(); i++)
    p[i] = p[i - 1] * 10;
    vector<int> res;
    long long cur = 0;
    int cur_digits = 0;
    for (int i = 0; i < (int) a.size(); i++) {
    cur += a[i] * p[cur_digits];
    cur_digits += old_digits;
    while (cur_digits >= new_digits) {
    res.push_back(int(cur % p[new_digits]));
    cur /= p[new_digits];
    cur_digits -= new_digits;
    }
    }
    res.push_back((int) cur);
    while (!res.empty() && !res.back())
    res.pop_back();
    return res;
    }

    typedef vector<long long> vll;

    static vll karatsubaMultiply(const vll &a, const vll &b) {
    int n = a.size();
    vll res(n + n);
    if (n <= 32) {
    for (int i = 0; i < n; i++)
    for (int j = 0; j < n; j++)
    res[i + j] += a[i] * b[j];
    return res;
    }

    int k = n >> 1;
    vll a1(a.begin(), a.begin() + k);
    vll a2(a.begin() + k, a.end());
    vll b1(b.begin(), b.begin() + k);
    vll b2(b.begin() + k, b.end());

    vll a1b1 = karatsubaMultiply(a1, b1);
    vll a2b2 = karatsubaMultiply(a2, b2);

    for (int i = 0; i < k; i++)
    a2[i] += a1[i];
    for (int i = 0; i < k; i++)
    b2[i] += b1[i];

    vll r = karatsubaMultiply(a2, b2);
    for (int i = 0; i < (int) a1b1.size(); i++)
    r[i] -= a1b1[i];
    for (int i = 0; i < (int) a2b2.size(); i++)
    r[i] -= a2b2[i];

    for (int i = 0; i < (int) r.size(); i++)
    res[i + k] += r[i];
    for (int i = 0; i < (int) a1b1.size(); i++)
    res[i] += a1b1[i];
    for (int i = 0; i < (int) a2b2.size(); i++)
    res[i + n] += a2b2[i];
    return res;
    }

    bigint operator*(const bigint &v) const {
    vector<int> a6 = convert_base(this->a, base_digits, 6);
    vector<int> b6 = convert_base(v.a, base_digits, 6);
    vll a(a6.begin(), a6.end());
    vll b(b6.begin(), b6.end());
    while (a.size() < b.size())
    a.push_back(0);
    while (b.size() < a.size())
    b.push_back(0);
    while (a.size() & (a.size() - 1))
    a.push_back(0), b.push_back(0);
    vll c = karatsubaMultiply(a, b);
    bigint res;
    res.sign = sign * v.sign;
    for (int i = 0, carry = 0; i < (int) c.size(); i++) {
    long long cur = c[i] + carry;
    res.a.push_back((int) (cur % 1000000));
    carry = (int) (cur / 1000000);
    }
    res.a = convert_base(res.a, 6, base_digits);
    res.trim();
    return res;
    }
    return -(v - *this);
    }
    return *this + (-v);
    }

    void operator*=(int v) {
    if (v < 0)
    sign = -sign, v = -v;
    for (int i = 0, carry = 0; i < (int) a.size() || carry; ++i) {
    if (i == (int) a.size())
    a.push_back(0);
    long long cur = a[i] * (long long) v + carry;
    carry = (int) (cur / base);
    a[i] = (int) (cur % base);
    //asm("divl %%ecx" : "=a"(carry), "=d"(a[i]) : "A"(cur), "c"(base));
    }
    trim();
    }

    bigint operator*(int v) const {
    bigint res = *this;
    res *= v;
    return res;
    }

    friend pair<bigint, bigint> divmod(const bigint &a1, const bigint &b1) {
    int norm = base / (b1.a.back() + 1);
    bigint a = a1.abs() * norm;
    bigint b = b1.abs() * norm;
    bigint q, r;
    q.a.resize(a.a.size());

    for (int i = a.a.size() - 1; i >= 0; i--) {
    r *= base;
    r += a.a[i];
    int s1 = r.a.size() <= b.a.size() ? 0 : r.a[b.a.size()];
    int s2 = r.a.size() <= b.a.size() - 1 ? 0 : r.a[b.a.size() - 1];
    int d = ((long long) base * s1 + s2) / b.a.back();
    r -= b * d;
    while (r < 0)
    r += b, --d;
    q.a[i] = d;
    }

    q.sign = a1.sign * b1.sign;
    r.sign = a1.sign;
    q.trim();
    r.trim();
    return make_pair(q, r / norm);
    }

    bigint operator/(const bigint &v) const {
    return divmod(*this, v).first;
    }

    bigint operator%(const bigint &v) const {
    return divmod(*this, v).second;
    }

    void operator/=(int v) {
    if (v < 0)
    sign = -sign, v = -v;
    for (int i = (int) a.size() - 1, rem = 0; i >= 0; --i) {
    long long cur = a[i] + rem * (long long) base;
    a[i] = (int) (cur / v);
    rem = (int) (cur % v);
    }
    trim();
    }

    bigint operator/(int v) const {
    bigint res = *this;
    res /= v;
    return res;
    }

    int operator%(int v) const {
    if (v < 0)
    v = -v;
    int m = 0;
    for (int i = a.size() - 1; i >= 0; --i)
    m = (a[i] + m * (long long) base) % v;
    return m * sign;
    }

    void operator+=(const bigint &v) {
    *this = *this + v;
    }
    void operator-=(const bigint &v) {
    *this = *this - v;
    }
    void operator*=(const bigint &v) {
    *this = *this * v;
    }
    void operator/=(const bigint &v) {
    *this = *this / v;
    }

    bool operator<(const bigint &v) const {
    if (sign != v.sign)
    return sign < v.sign;
    if (a.size() != v.a.size())
    return a.size() * sign < v.a.size() * v.sign;
    for (int i = a.size() - 1; i >= 0; i--)
    if (a[i] != v.a[i])
    return a[i] * sign < v.a[i] * sign;
    return false;
    }

    bool operator>(const bigint &v) const {
    return v < *this;
    }
    bool operator<=(const bigint &v) const {
    return !(v < *this);
    }
    bool operator>=(const bigint &v) const {
    return !(*this < v);
    }
    bool operator==(const bigint &v) const {
    return !(*this < v) && !(v < *this);
    }
    bool operator!=(const bigint &v) const {
    return *this < v || v < *this;
    }

    void trim() {
    while (!a.empty() && !a.back())
    a.pop_back();
    if (a.empty())
    sign = 1;
    }

    bool isZero() const {
    return a.empty() || (a.size() == 1 && !a[0]);
    }

    bigint operator-() const {
    bigint res = *this;
    res.sign = -sign;
    return res;
    }

    bigint abs() const {
    bigint res = *this;
    res.sign *= res.sign;
    return res;
    }

    long long longValue() const {
    long long res = 0;
    for (int i = a.size() - 1; i >= 0; i--)
    res = res * base + a[i];
    return res * sign;
    }

    friend bigint gcd(const bigint &a, const bigint &b) {
    return b.isZero() ? a : gcd(b, a % b);
    }
    friend bigint lcm(const bigint &a, const bigint &b) {
    return a / gcd(a, b) * b;
    }

    void read(const string &s) {
    sign = 1;
    a.clear();
    int pos = 0;
    while (pos < (int) s.size() && (s[pos] == '-' || s[pos] == '+')) {
    if (s[pos] == '-')
    sign = -sign;
    ++pos;
    }
    for (int i = s.size() - 1; i >= pos; i -= base_digits) {
    int x = 0;
    for (int j = max(pos, i - base_digits + 1); j <= i; j++)
    x = x * 10 + s[j] - '0';
    a.push_back(x);
    }
    trim();
    }

    friend istream& operator>>(istream &stream, bigint &v) {
    string s;
    stream >> s;
    v.read(s);
    return stream;
    }

    friend ostream& operator<<(ostream &stream, const bigint &v) {
    if (v.sign == -1)
    stream << '-';
    stream << (v.a.empty() ? 0 : v.a.back());
    for (int i = (int) v.a.size() - 2; i >= 0; --i)
    stream << setw(base_digits) << setfill('0') << v.a[i];
    return stream;
    }

    static vector<int> convert_base(const vector<int> &a, int old_digits, int new_digits) {
    vector<long long> p(max(old_digits, new_digits) + 1);
    p[0] = 1;
    for (int i = 1; i < (int) p.size(); i++)
    p[i] = p[i - 1] * 10;
    vector<int> res;
    long long cur = 0;
    int cur_digits = 0;
    for (int i = 0; i < (int) a.size(); i++) {
    cur += a[i] * p[cur_digits];
    cur_digits += old_digits;
    while (cur_digits >= new_digits) {
    res.push_back(int(cur % p[new_digits]));
    cur /= p[new_digits];
    cur_digits -= new_digits;
    }
    }
    res.push_back((int) cur);
    while (!res.empty() && !res.back())
    res.pop_back();
    return res;
    }

    typedef vector<long long> vll;

    static vll karatsubaMultiply(const vll &a, const vll &b) {
    int n = a.size();
    vll res(n + n);
    if (n <= 32) {
    for (int i = 0; i < n; i++)
    for (int j = 0; j < n; j++)
    res[i + j] += a[i] * b[j];
    return res;
    }

    int k = n >> 1;
    vll a1(a.begin(), a.begin() + k);
    vll a2(a.begin() + k, a.end());
    vll b1(b.begin(), b.begin() + k);
    vll b2(b.begin() + k, b.end());

    vll a1b1 = karatsubaMultiply(a1, b1);
    vll a2b2 = karatsubaMultiply(a2, b2);

    for (int i = 0; i < k; i++)
    a2[i] += a1[i];
    for (int i = 0; i < k; i++)
    b2[i] += b1[i];

    vll r = karatsubaMultiply(a2, b2);
    for (int i = 0; i < (int) a1b1.size(); i++)
    r[i] -= a1b1[i];
    for (int i = 0; i < (int) a2b2.size(); i++)
    r[i] -= a2b2[i];

    for (int i = 0; i < (int) r.size(); i++)
    res[i + k] += r[i];
    for (int i = 0; i < (int) a1b1.size(); i++)
    res[i] += a1b1[i];
    for (int i = 0; i < (int) a2b2.size(); i++)
    res[i + n] += a2b2[i];
    return res;
    }

    bigint operator*(const bigint &v) const {
    vector<int> a6 = convert_base(this->a, base_digits, 6);
    vector<int> b6 = convert_base(v.a, base_digits, 6);
    vll a(a6.begin(), a6.end());
    vll b(b6.begin(), b6.end());
    while (a.size() < b.size())
    a.push_back(0);
    while (b.size() < a.size())
    b.push_back(0);
    while (a.size() & (a.size() - 1))
    a.push_back(0), b.push_back(0);
    vll c = karatsubaMultiply(a, b);
    bigint res;
    res.sign = sign * v.sign;
    for (int i = 0, carry = 0; i < (int) c.size(); i++) {
    long long cur = c[i] + carry;
    res.a.push_back((int) (cur % 1000000));
    carry = (int) (cur / 1000000);
    }
    res.a = convert_base(res.a, 6, base_digits);
    res.trim();
    return res;
    }
    };
    }
    };
    /*
    ####################### THE BIG INT ##########################
    ######################################################################
    */
  5. @ar-pa ar-pa created this gist Jan 3, 2016.
    363 changes: 363 additions & 0 deletions BigInt.cpp
    View file
    Original file line number Diff line number Diff line change
    @@ -0,0 +1,363 @@
    const int base = 1000000000;
    const int base_digits = 9;
    struct bigint {
    vector<int> a;
    int sign;
    /*<arpa>*/
    int size(){
    if(a.empty())return 0;
    int ans=(a.size()-1)*base_digits;
    int ca=a.back();
    while(ca)
    ans++,ca/=10;
    return ans;
    }
    bigint operator ^(const bigint &v){
    bigint ans=1,a=*this,b=v;
    while(!b.isZero()){
    if(b%2)
    ans*=a;
    a*=a,b/=2;
    }
    return ans;
    }
    /*</arpa>*/
    bigint() :
    sign(1) {
    }

    bigint(long long v) {
    *this = v;
    }

    bigint(const string &s) {
    read(s);
    }

    void operator=(const bigint &v) {
    sign = v.sign;
    a = v.a;
    }

    void operator=(long long v) {
    sign = 1;
    if (v < 0)
    sign = -1, v = -v;
    for (; v > 0; v = v / base)
    a.push_back(v % base);
    }

    bigint operator+(const bigint &v) const {
    if (sign == v.sign) {
    bigint res = v;

    for (int i = 0, carry = 0; i < (int) max(a.size(), v.a.size()) || carry; ++i) {
    if (i == (int) res.a.size())
    res.a.push_back(0);
    res.a[i] += carry + (i < (int) a.size() ? a[i] : 0);
    carry = res.a[i] >= base;
    if (carry)
    res.a[i] -= base;
    }
    return res;
    }
    return *this - (-v);
    }

    bigint operator-(const bigint &v) const {
    if (sign == v.sign) {
    if (abs() >= v.abs()) {
    bigint res = *this;
    for (int i = 0, carry = 0; i < (int) v.a.size() || carry; ++i) {
    res.a[i] -= carry + (i < (int) v.a.size() ? v.a[i] : 0);
    carry = res.a[i] < 0;
    if (carry)
    res.a[i] += base;
    }
    res.trim();
    return res;
    }
    return -(v - *this);
    }
    return *this + (-v);
    }

    void operator*=(int v) {
    if (v < 0)
    sign = -sign, v = -v;
    for (int i = 0, carry = 0; i < (int) a.size() || carry; ++i) {
    if (i == (int) a.size())
    a.push_back(0);
    long long cur = a[i] * (long long) v + carry;
    carry = (int) (cur / base);
    a[i] = (int) (cur % base);
    //asm("divl %%ecx" : "=a"(carry), "=d"(a[i]) : "A"(cur), "c"(base));
    }
    trim();
    }

    bigint operator*(int v) const {
    bigint res = *this;
    res *= v;
    return res;
    }

    friend pair<bigint, bigint> divmod(const bigint &a1, const bigint &b1) {
    int norm = base / (b1.a.back() + 1);
    bigint a = a1.abs() * norm;
    bigint b = b1.abs() * norm;
    bigint q, r;
    q.a.resize(a.a.size());

    for (int i = a.a.size() - 1; i >= 0; i--) {
    r *= base;
    r += a.a[i];
    int s1 = r.a.size() <= b.a.size() ? 0 : r.a[b.a.size()];
    int s2 = r.a.size() <= b.a.size() - 1 ? 0 : r.a[b.a.size() - 1];
    int d = ((long long) base * s1 + s2) / b.a.back();
    r -= b * d;
    while (r < 0)
    r += b, --d;
    q.a[i] = d;
    }

    q.sign = a1.sign * b1.sign;
    r.sign = a1.sign;
    q.trim();
    r.trim();
    return make_pair(q, r / norm);
    }

    bigint operator/(const bigint &v) const {
    return divmod(*this, v).first;
    }

    bigint operator%(const bigint &v) const {
    return divmod(*this, v).second;
    }

    void operator/=(int v) {
    if (v < 0)
    sign = -sign, v = -v;
    for (int i = (int) a.size() - 1, rem = 0; i >= 0; --i) {
    long long cur = a[i] + rem * (long long) base;
    a[i] = (int) (cur / v);
    rem = (int) (cur % v);
    }
    trim();
    }

    bigint operator/(int v) const {
    bigint res = *this;
    res /= v;
    return res;
    }

    int operator%(int v) const {
    if (v < 0)
    v = -v;
    int m = 0;
    for (int i = a.size() - 1; i >= 0; --i)
    m = (a[i] + m * (long long) base) % v;
    return m * sign;
    }

    void operator+=(const bigint &v) {
    *this = *this + v;
    }
    void operator-=(const bigint &v) {
    *this = *this - v;
    }
    void operator*=(const bigint &v) {
    *this = *this * v;
    }
    void operator/=(const bigint &v) {
    *this = *this / v;
    }

    bool operator<(const bigint &v) const {
    if (sign != v.sign)
    return sign < v.sign;
    if (a.size() != v.a.size())
    return a.size() * sign < v.a.size() * v.sign;
    for (int i = a.size() - 1; i >= 0; i--)
    if (a[i] != v.a[i])
    return a[i] * sign < v.a[i] * sign;
    return false;
    }

    bool operator>(const bigint &v) const {
    return v < *this;
    }
    bool operator<=(const bigint &v) const {
    return !(v < *this);
    }
    bool operator>=(const bigint &v) const {
    return !(*this < v);
    }
    bool operator==(const bigint &v) const {
    return !(*this < v) && !(v < *this);
    }
    bool operator!=(const bigint &v) const {
    return *this < v || v < *this;
    }

    void trim() {
    while (!a.empty() && !a.back())
    a.pop_back();
    if (a.empty())
    sign = 1;
    }

    bool isZero() const {
    return a.empty() || (a.size() == 1 && !a[0]);
    }

    bigint operator-() const {
    bigint res = *this;
    res.sign = -sign;
    return res;
    }

    bigint abs() const {
    bigint res = *this;
    res.sign *= res.sign;
    return res;
    }

    long long longValue() const {
    long long res = 0;
    for (int i = a.size() - 1; i >= 0; i--)
    res = res * base + a[i];
    return res * sign;
    }

    friend bigint gcd(const bigint &a, const bigint &b) {
    return b.isZero() ? a : gcd(b, a % b);
    }
    friend bigint lcm(const bigint &a, const bigint &b) {
    return a / gcd(a, b) * b;
    }

    void read(const string &s) {
    sign = 1;
    a.clear();
    int pos = 0;
    while (pos < (int) s.size() && (s[pos] == '-' || s[pos] == '+')) {
    if (s[pos] == '-')
    sign = -sign;
    ++pos;
    }
    for (int i = s.size() - 1; i >= pos; i -= base_digits) {
    int x = 0;
    for (int j = max(pos, i - base_digits + 1); j <= i; j++)
    x = x * 10 + s[j] - '0';
    a.push_back(x);
    }
    trim();
    }

    friend istream& operator>>(istream &stream, bigint &v) {
    string s;
    stream >> s;
    v.read(s);
    return stream;
    }

    friend ostream& operator<<(ostream &stream, const bigint &v) {
    if (v.sign == -1)
    stream << '-';
    stream << (v.a.empty() ? 0 : v.a.back());
    for (int i = (int) v.a.size() - 2; i >= 0; --i)
    stream << setw(base_digits) << setfill('0') << v.a[i];
    return stream;
    }

    static vector<int> convert_base(const vector<int> &a, int old_digits, int new_digits) {
    vector<long long> p(max(old_digits, new_digits) + 1);
    p[0] = 1;
    for (int i = 1; i < (int) p.size(); i++)
    p[i] = p[i - 1] * 10;
    vector<int> res;
    long long cur = 0;
    int cur_digits = 0;
    for (int i = 0; i < (int) a.size(); i++) {
    cur += a[i] * p[cur_digits];
    cur_digits += old_digits;
    while (cur_digits >= new_digits) {
    res.push_back(int(cur % p[new_digits]));
    cur /= p[new_digits];
    cur_digits -= new_digits;
    }
    }
    res.push_back((int) cur);
    while (!res.empty() && !res.back())
    res.pop_back();
    return res;
    }

    typedef vector<long long> vll;

    static vll karatsubaMultiply(const vll &a, const vll &b) {
    int n = a.size();
    vll res(n + n);
    if (n <= 32) {
    for (int i = 0; i < n; i++)
    for (int j = 0; j < n; j++)
    res[i + j] += a[i] * b[j];
    return res;
    }

    int k = n >> 1;
    vll a1(a.begin(), a.begin() + k);
    vll a2(a.begin() + k, a.end());
    vll b1(b.begin(), b.begin() + k);
    vll b2(b.begin() + k, b.end());

    vll a1b1 = karatsubaMultiply(a1, b1);
    vll a2b2 = karatsubaMultiply(a2, b2);

    for (int i = 0; i < k; i++)
    a2[i] += a1[i];
    for (int i = 0; i < k; i++)
    b2[i] += b1[i];

    vll r = karatsubaMultiply(a2, b2);
    for (int i = 0; i < (int) a1b1.size(); i++)
    r[i] -= a1b1[i];
    for (int i = 0; i < (int) a2b2.size(); i++)
    r[i] -= a2b2[i];

    for (int i = 0; i < (int) r.size(); i++)
    res[i + k] += r[i];
    for (int i = 0; i < (int) a1b1.size(); i++)
    res[i] += a1b1[i];
    for (int i = 0; i < (int) a2b2.size(); i++)
    res[i + n] += a2b2[i];
    return res;
    }

    bigint operator*(const bigint &v) const {
    vector<int> a6 = convert_base(this->a, base_digits, 6);
    vector<int> b6 = convert_base(v.a, base_digits, 6);
    vll a(a6.begin(), a6.end());
    vll b(b6.begin(), b6.end());
    while (a.size() < b.size())
    a.push_back(0);
    while (b.size() < a.size())
    b.push_back(0);
    while (a.size() & (a.size() - 1))
    a.push_back(0), b.push_back(0);
    vll c = karatsubaMultiply(a, b);
    bigint res;
    res.sign = sign * v.sign;
    for (int i = 0, carry = 0; i < (int) c.size(); i++) {
    long long cur = c[i] + carry;
    res.a.push_back((int) (cur % 1000000));
    carry = (int) (cur / 1000000);
    }
    res.a = convert_base(res.a, 6, base_digits);
    res.trim();
    return res;
    }
    };