Bigint.cpp

const int maxn = 1e2 + 14, lg = 15;
const int base = 1000000000;
const int base_digits = 9;
struct bigint {
  vi a;
  int sign;

  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;
    a.clear();
    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;
  }

  void operator*=(long long v) {
    if (v < 0) sign = -sign, v = -v;
    if (v > base) {
      *this = *this * (v / base) * base +
              *this * (v % base);
      return;
    }
    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;
    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;
  }
};