# -*- mode: snippet -*-
# name: bigInt
# contributor: Bhuvnesh Jain
# key: bigint
# --

//Big Integer library for C++, taken from github, don't remember the source

#include <bits/stdc++.h>
using namespace std;

// base and base_digits must be consistent
const int base = 1000000000;
const int base_digits = 9;

//contains implementations for all basic operators, arithmetic, logical and compartor
//contains implementation for sqrt function as well
//cin and cout operators also overloaded
//gcd and lcm also included
struct bigint {
	vector<int> z;
	int sign;
	bigint() : sign(1) { }
	bigint(long long v) { *this = v; }
	bigint(const string &s) { read(s); }

	void operator=(const bigint &v) {
		sign = v.sign;
		z = v.z;
	}
	void operator=(long long v) {
		sign = 1;
		if (v < 0) sign = -1, v = -v;
		z.clear();
		for (; v > 0; v = v / base) z.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(z.size(), v.z.size()) || carry; ++i) {
				if (i == (int) res.z.size())
					res.z.push_back(0);
				res.z[i] += carry + (i < (int) z.size() ? z[i] : 0);
				carry = res.z[i] >= base;
				if (carry)
					res.z[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.z.size() || carry; ++i) {
					res.z[i] -= carry + (i < (int) v.z.size() ? v.z[i] : 0);
					carry = res.z[i] < 0;
					if (carry) res.z[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) z.size() || carry; ++i) {
			if (i == (int) z.size())
				z.push_back(0);
			long long cur = z[i] * (long long) v + carry;
			carry = (int) (cur / base);
			z[i] = (int) (cur % 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.z.back() + 1);
		bigint a = a1.abs() * norm;
		bigint b = b1.abs() * norm;
		bigint q, r;
		q.z.resize(a.z.size());
		for (int i = a.z.size() - 1; i >= 0; i--) {
			r *= base;
			r += a.z[i];
			int s1 = b.z.size() < r.z.size() ? r.z[b.z.size()] : 0;
			int s2 = b.z.size() - 1 < r.z.size() ? r.z[b.z.size() - 1] : 0;
			int d = ((long long) s1 * base + s2) / b.z.back();
			r -= b * d;
			while (r < 0)
				r += b, --d;
			q.z[i] = d;
		}
		q.sign = a1.sign * b1.sign;
		r.sign = a1.sign;
		q.trim();
		r.trim();
		return make_pair(q, r / norm);
	}
	friend bigint sqrt(const bigint &a1) {
		bigint a = a1;
		while (a.z.empty() || a.z.size() % 2 == 1) a.z.push_back(0);
		int n = a.z.size();
		int firstDigit = (int) sqrt((double) a.z[n - 1] * base + a.z[n - 2]);
		int norm = base / (firstDigit + 1);
		a *= norm;
		a *= norm;
		while (a.z.empty() || a.z.size() % 2 == 1)
			a.z.push_back(0);
		bigint r = (long long) a.z[n - 1] * base + a.z[n - 2];
		firstDigit = (int) sqrt((double) a.z[n - 1] * base + a.z[n - 2]);
		int q = firstDigit;
		bigint res;
		for(int j = n / 2 - 1; j >= 0; j--) {
			for(; ; --q) {
				bigint r1 = (r - (res*2*base+q)*q)*base*base + (j > 0 ? (long long)a.z[2*j-1]*base + a.z[2*j-2] : 0);
				if (r1 >= 0) {
					r = r1;
					break;
				}
			}
			res *= base;
			res += q;
			if (j > 0) {
				int d1 = res.z.size() + 2 < r.z.size() ? r.z[res.z.size() + 2] : 0;
				int d2 = res.z.size() + 1 < r.z.size() ? r.z[res.z.size() + 1] : 0;
				int d3 = res.z.size() < r.z.size() ? r.z[res.z.size()] : 0;
				q = ((long long) d1 * base * base + (long long) d2 * base + d3) / (firstDigit * 2);
			}
		}
		res.trim();
		return res / 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) z.size() - 1, rem = 0; i >= 0; --i) {
			long long cur = z[i] + rem * (long long) base;
			z[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 = z.size() - 1; i >= 0; --i)
			m = (z[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 (z.size() != v.z.size())
			return z.size() * sign < v.z.size() * v.sign;
		for (int i = z.size() - 1; i >= 0; i--)
			if (z[i] != v.z[i])
				return z[i] * sign < v.z[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 (!z.empty() && z.back() == 0)
			z.pop_back();
		if (z.empty())
			sign = 1;
	}
	bool isZero() const {
		return z.empty() || (z.size() == 1 && !z[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 = z.size() - 1; i >= 0; i--)
			res = res * base + z[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;
		z.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';
			z.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.z.empty() ? 0 : v.z.back());
		for (int i = (int) v.z.size() - 2; i >= 0; --i)
			stream << setw(base_digits) << setfill('0') << v.z[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() == 0)
			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->z, base_digits, 6);
		vector<int> b6 = convert_base(v.z, 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.z.push_back((int) (cur % 1000000));
			carry = (int) (cur / 1000000);
		}
		res.z = convert_base(res.z, 6, base_digits);
		res.trim();
		return res;
	}
};

bigint random_bigint(int n) {
	string s;
	for (int i = 0; i < n; i++) {
		s += rand() % 10 + '0';
	}
	return bigint(s);
}

// random tests
int main() {
	for(int i = 0; i < 1000; i++) {
		cout << i << endl;
		int n = rand() % 100 + 1;
		bigint a = random_bigint(n);
		bigint res = sqrt(a);
		bigint xx = res * res;
		bigint yy = (res + 1) * (res + 1);

		if (xx > a || yy <= a) {
			cout << a << " " << res << endl;
			break;
		}

		int m = rand() % n + 1;
		bigint b = random_bigint(m) + 1;
		res = a / b;
		xx = res * b;
		yy = b * (res + 1);

		if (xx > a || yy <= a) {
			cout << a << " " << b << " " << res << endl;
			break;
		}
	}

	bigint a = random_bigint(10000);
	bigint b = random_bigint(2000);
	clock_t start = clock();
	bigint c = a / b;
	fprintf(stdout, "time=%.3lfsec\n", 0.001 * (clock() - start));

	bigint x = 5;
	x = 6;
	cout << x << endl;
}
