#define _USE_MATH_DEFINES #include using namespace std; #define FOR(i,m,n) for(int i=(m);i<(n);++i) #define REP(i,n) FOR(i,0,n) #define ALL(v) (v).begin(),(v).end() using ll = long long; constexpr int INF = 0x3f3f3f3f; constexpr long long LINF = 0x3f3f3f3f3f3f3f3fLL; constexpr double EPS = 1e-8; constexpr int MOD = 998244353; // constexpr int MOD = 1000000007; constexpr int DY4[]{1, 0, -1, 0}, DX4[]{0, -1, 0, 1}; constexpr int DY8[]{1, 1, 0, -1, -1, -1, 0, 1}; constexpr int DX8[]{0, -1, -1, -1, 0, 1, 1, 1}; template inline bool chmax(T& a, U b) { return a < b ? (a = b, true) : false; } template inline bool chmin(T& a, U b) { return a > b ? (a = b, true) : false; } struct IOSetup { IOSetup() { std::cin.tie(nullptr); std::ios_base::sync_with_stdio(false); std::cout << fixed << setprecision(20); } } iosetup; template // B = 10^{LogB} struct BigInt { int sgn; std::vector data; BigInt(const long long val = 0) { *this = val; } BigInt(const std::string& s) { *this = s; } std::vector convert_base(const int next_log_b, const int next_b) const { assert(next_b == static_cast(std::round(std::pow(10, next_log_b)))); const int max_base = std::max(LogB, next_log_b); std::vector p(max_base + 1, 1); for (int i = 1; i <= max_base; ++i) { p[i] = p[i - 1] * 10; } std::vector res; long long cur_val = 0; int cur_log_b = 0; for (const int e : data) { cur_val += p[cur_log_b] * e; cur_log_b += LogB; for (; cur_log_b >= next_log_b; cur_log_b -= next_log_b) { res.emplace_back(cur_val % next_b); cur_val /= next_b; } } res.emplace_back(cur_val); while (!res.empty() && res.back() == 0) res.pop_back(); return res; } int digit_sum() const { assert(sgn == 1); int res = 0; for (char c : to_string()) res += c - '0'; return res; } int length() const { if (data.empty()) return 0; int res = LogB * (data.size() - 1); for (int tmp = data.back(); tmp > 0; tmp /= 10) { ++res; } return res; } BigInt pow(BigInt exponent) const { BigInt res = 1, tmp = *this; for (; exponent > 0; exponent /= 2) { if (exponent.data.front() & 1) res *= tmp; tmp *= tmp; } return res; } long long to_llong() const { assert(*this >= std::numeric_limits::min() && *this <= std::numeric_limits::max()); long long res = 0; for (int i = static_cast(data.size()) - 1; i >= 0; --i) { res = res * B + data[i]; } return res; } std::string to_string() const { std::stringstream ss; ss << *this; std::string res; ss >> res; return res; } void trim() { while (!data.empty() && data.back() == 0) data.pop_back(); if (data.empty()) sgn = 1; } BigInt& operator=(long long val) { if (val < 0) { sgn = -1; val = -val; } else { sgn = 1; } data.clear(); for (; val > 0; val /= B) { data.emplace_back(val % B); } return *this; } BigInt& operator=(const std::string& s) { sgn = 1; data.clear(); if (!s.empty()) { int tail = 0; if (s.front() == '-') { sgn = -1; tail = 1; } else if (s.front() == '+') { tail = 1; } for (int i = s.length() - 1; i >= tail; i -= LogB) { int val = 0; for (int j = std::max(tail, i - LogB + 1); j <= i; ++j) { val = val * 10 + (s[j] - '0'); } data.emplace_back(val); } } trim(); return *this; } BigInt& operator=(const BigInt& x) = default; BigInt& operator+=(const BigInt& x) { if (sgn != x.sgn) return *this -= -x; if (data.size() < x.data.size()) data.resize(x.data.size(), 0); bool carry = false; for (int i = 0; i < x.data.size() || carry; ++i) { if (i == data.size()) data.emplace_back(0); data[i] += (i < x.data.size() ? x.data[i] : 0) + carry; if (data[i] >= B) { carry = true; data[i] -= B; } else { carry = false; } } return *this; } BigInt& operator-=(const BigInt& x) { if (sgn != x.sgn) return *this += -x; if ((sgn == 1 ? *this : -*this) < (x.sgn == 1 ? x : -x)) { return *this = -(x - *this); } bool carry = false; for (int i = 0; i < data.size() || carry; ++i) { data[i] -= (i < x.data.size() ? x.data[i] : 0) + carry; if (data[i] < 0) { carry = true; data[i] += B; } else { carry = false; } } trim(); return *this; } BigInt& operator*=(const BigInt& x) { constexpr int next_log_b = 6, next_b = 1000000; std::vector this6 = convert_base(next_log_b, next_b); std::vector x6 = x.convert_base(next_log_b, next_b); std::vector res = karatsuba(&this6, 0, this6.size(), &x6, 0, x6.size()); for (int i = 0; i < res.size(); ++i) { const long long quo = res[i] / next_b; if (quo > 0) { if (i + 1 == res.size()) { res.emplace_back(quo); } else { res[i + 1] += quo; } res[i] %= next_b; } } std::string s = (sgn * x.sgn == 1 ? "+" : "-"); for (int i = static_cast(res.size()) - 1; i >= 0; --i) { const std::string tmp = std::to_string(res[i]); s += std::string(next_log_b - tmp.length(), '0') + tmp; } return *this = s; } BigInt& operator/=(int x) { return *this = divide(x).first; } BigInt& operator/=(const BigInt& x) { return *this = divide(x).first; } BigInt& operator%=(int x) { return *this = divide(x).second; } BigInt& operator%=(const BigInt& x) { return *this = divide(x).second; } bool operator==(const BigInt& x) const { if (sgn != x.sgn || data.size() != x.data.size()) return false; const int n = data.size(); for (int i = 0; i < n; ++i) { if (data[i] != x.data[i]) return false; } return true; } bool operator!=(const BigInt& x) const { return !(*this == x); } bool operator<(const BigInt& x) const { if (sgn != x.sgn) return sgn < x.sgn; if (data.size() != x.data.size()) { return sgn * data.size() < x.sgn * x.data.size(); } for (int i = static_cast(data.size()) - 1; i >= 0; --i) { if (data[i] != x.data[i]) return data[i] * sgn < x.data[i] * x.sgn; } return false; } bool operator<=(const BigInt& x) const { return !(x < *this); } bool operator>(const BigInt& x) const { return x < *this; } bool operator>=(const BigInt& x) const { return !(*this < x); } BigInt& operator++() { return *this += 1; } BigInt operator++(int) { const BigInt res = *this; ++*this; return res; } BigInt& operator--() { return *this -= 1; } BigInt operator--(int) { const BigInt res = *this; --*this; return res; } BigInt operator+() const { return *this; } BigInt operator-() const { BigInt res = *this; res.sgn = -res.sgn; return res; } BigInt operator+(const BigInt& x) const { return BigInt(*this) += x; } BigInt operator-(const BigInt& x) const { return BigInt(*this) -= x; } BigInt operator*(const BigInt& x) const { return BigInt(*this) *= x; } BigInt operator/(int x) const { return BigInt(*this) /= x; } BigInt operator/(const BigInt& x) const { return BigInt(*this) /= x; } BigInt operator%(int x) const { return BigInt(*this) %= x; } BigInt operator%(const BigInt& x) const { return BigInt(*this) %= x; } friend std::ostream& operator<<(std::ostream& os, const BigInt& x) { if (x.sgn == -1) os << '-'; os << (x.data.empty() ? 0 : x.data.back()); for (int i = static_cast(x.data.size()) - 2; i >= 0; --i) { os << std::setw(LogB) << std::setfill('0') << x.data[i]; } return os; } friend std::istream& operator>>(std::istream& is, BigInt& x) { std::string s; is >> s; x = s; return is; } private: std::vector karatsuba( std::vector* a, const int a_l, const int a_r, std::vector* b, const int b_l, const int b_r) const { const int a_len = a_r - a_l, b_len = b_r - b_l; if (a_len < b_len) return karatsuba(b, b_l, b_r, a, a_l, a_r); std::vector res(a_len + b_len, 0); if (b_len <= 32) { for (int i = a_l; i < a_r; ++i) { for (int j = b_l; j < b_r; ++j) { res[(i - a_l) + (j - b_l)] += (*a)[i] * (*b)[j]; } } } else { const int mid = (a_len + 1) / 2, n = std::min(a_len, mid); for (int i = a_l; i + mid < a_r; ++i) { (*a)[i] += (*a)[i + mid]; } for (int i = b_l; i + mid < b_r; ++i) { (*b)[i] += (*b)[i + mid]; } std::vector tmp = karatsuba(a, a_l, a_l + mid, b, b_l, b_l + n); std::copy(tmp.begin(), tmp.end(), std::next(res.begin(), mid)); for (int i = a_l; i + mid < a_r; ++i) { (*a)[i] -= (*a)[i + mid]; } for (int i = b_l; i + mid < b_r; ++i) { (*b)[i] -= (*b)[i + mid]; } tmp = karatsuba(a, a_l, a_l + mid, b, b_l, b_l + n); for (int i = 0; i < tmp.size(); ++i) { res[i] += tmp[i]; res[mid + i] -= tmp[i]; } tmp = karatsuba(a, a_l + mid, a_r, b, b_l + n, b_r); for (int i = 0; i < tmp.size(); ++i) { res[mid + i] -= tmp[i]; res[(mid << 1) + i] += tmp[i]; } } while (!res.empty() && res.back() == 0) res.pop_back(); return res; } std::pair divide(int x) const { assert(x != 0); BigInt dividend = *this; if (x < 0) { dividend.sgn = -dividend.sgn; x = -x; } long long rem = 0; for (int i = static_cast(dividend.data.size()) - 1; i >= 0; --i) { const long long tmp = rem * B + dividend.data[i]; dividend.data[i] = tmp / x; rem = tmp % x; } dividend.trim(); return {dividend, static_cast(rem)}; } std::pair divide(const BigInt& x) const { assert(!x.data.empty()); const int k = B / (x.data.back() + 1); const BigInt dividend = (sgn == 1 ? *this : -*this) * k; const BigInt divisor = (x.sgn == 1 ? x : -x) * k; BigInt quo, rem = 0; quo.data.resize(dividend.data.size()); const int n = divisor.data.size(); for (int i = static_cast(dividend.data.size()) - 1; i >= 0; --i) { rem.data.emplace(rem.data.begin(), dividend.data[i]); quo.data[i] = ((n < rem.data.size() ? static_cast(rem.data[n]) * B : 0) + (n - 1 < rem.data.size() ? rem.data[n - 1] : 0)) / divisor.data.back(); rem -= divisor * quo.data[i]; while (rem.sgn == -1) { rem += divisor; --quo.data[i]; } } quo.sgn = sgn * x.sgn; quo.trim(); rem.sgn = sgn; rem.trim(); return {quo, rem / k}; } }; namespace std { template BigInt __gcd(BigInt a, BigInt b) { while (!b.data.empty()) std::swap(a %= b, b); return a; } template BigInt __lcm(const BigInt& a, const BigInt& b) { return a / std::__gcd(a, b) * b; } template BigInt abs(const BigInt& x) { return x.sgn == 1 ? x : -x; } template BigInt max(const BigInt& a, const BigInt& b) { return a < b ? b : a; } template BigInt min(const BigInt& a, const BigInt& b) { return a < b ? a : b; } } // namespace std int main() { using bigint = BigInt<>; bigint a, b; cin >> a >> b; cout << a + b << '\n'; return 0; }