#include using namespace std; #define pb push_back #define mp make_pair #define ALL(x) (x).begin(),(x).end() typedef long long ll; typedef pair pii; const int maxn = 3e5 + 70; const int INF = 0x3f3f3f3f; const ll inf = 0x3f3f3f3f3f3f3f3f; const int MOD = 1e9 + 7; const double eps = 1e-7; const double PI = acos(-1.0); // base and base_digits must be consistent const int base = 1000000000; const int base_digits = 9; struct bigint{ vector z; int sign; bigint() : sign(1) {} bigint(long long v) { *this = v; } bigint& operator=(long long v) { sign = v < 0 ? -1 : 1; v *= sign; z.clear(); for (; v > 0; v = v / base) z.push_back((int)(v % base)); return *this; } bigint(const string& s) { read(s); } bigint& operator+=(const bigint& other) { if (sign == other.sign) { for (int i = 0, carry = 0; i < other.z.size() || carry; ++i) { if (i == z.size()) z.push_back(0); z[i] += carry + (i < other.z.size() ? other.z[i] : 0); carry = z[i] >= base; if (carry) z[i] -= base; } } else if (other != 0 /* prevent infinite loop */) { *this -= -other; } return *this; } friend bigint operator+(bigint a, const bigint& b) { return a += b; } bigint& operator-=(const bigint& other) { if (sign == other.sign) { if (sign == 1 && *this >= other || sign == -1 && *this <= other) { for (int i = 0, carry = 0; i < other.z.size() || carry; ++i) { z[i] -= carry + (i < other.z.size() ? other.z[i] : 0); carry = z[i] < 0; if (carry) z[i] += base; } trim(); } else { *this = other - *this; this->sign = -this->sign; } } else { *this += -other; } return *this; } friend bigint operator-(bigint a, const bigint& b) { return a -= b; } bigint& operator*=(int v) { if (v < 0) sign = -sign, v = -v; for (int i = 0, carry = 0; i < z.size() || carry; ++i) { if (i == z.size()) z.push_back(0); long long cur = (long long)z[i] * v + carry; carry = (int)(cur / base); z[i] = (int)(cur % base); } trim(); return *this; } bigint operator*(int v) const { return bigint(*this) *= v; } friend pair 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 = (int)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 = (int)(((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{ 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 = (int)(((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; } bigint& 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(); return *this; } bigint operator/(int v) const { return bigint(*this) /= v; } int operator%(int v) const { if (v<0) v = -v; int m = 0; for (int i = (int)z.size() - 1; i >= 0; --i) m = (int)((z[i] + m*(long long)base) % v); return m * sign; } bigint& operator*=(const bigint& v) { *this = *this * v; return *this; } bigint& operator/=(const bigint& v) { *this = *this / v; return *this; } bool operator<(const bigint& v) const { if (sign != v.sign) return sign < v.sign; if (z.size() != v.z.size()) return z.size()*sign= 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(); } friend bigint operator-(bigint v) { if (!v.z.empty()) v.sign = -v.sign; return v; } bigint abs() const { return sign == 1 ? *this : -*this; } long long longValue() const { long long res = 0; for (int i = (int)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 < s.size() && (s[pos] == '-' || s[pos] == '+')) { if (s[pos] == '-') sign = -sign; ++pos; } for (int i = (int)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 convert_base(const vector& a, int old_digits, int new_digits) { vector p(max(old_digits, new_digits) + 1); p[0] = 1; for (int i = 1; i < p.size(); i++) p[i] = p[i - 1] * 10; vector res; long long cur = 0; int cur_digits = 0; for (int i = 0; i < a.size();i++) { int v = a[i]; cur += v * 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 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 a6 = convert_base(this->z, base_digits, 6); vector b6 = convert_base(v.z, base_digits, 6); vll a(a6.begin(), a6.end()); vll b(b6.begin(), b6.end()); while (a.size()>T; while(T--){ cin>>n>>a>>b; cout<