結果
| 問題 | No.2086 A+B問題 |
| ユーザー |
 anqooqie
|
| 提出日時 | 2022-11-05 20:21:15 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 2 ms / 2,000 ms |
| コード長 | 56,387 bytes |
| コンパイル時間 | 3,491 ms |
| コンパイル使用メモリ | 244,064 KB |
| 実行使用メモリ | 6,944 KB |
| 最終ジャッジ日時 | 2024-07-19 12:13:10 |
| 合計ジャッジ時間 | 4,400 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge3 |
（要ログイン）
テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 2 ms
6,812 KB |
| testcase_01 | AC | 2 ms
6,944 KB |
| testcase_02 | AC | 1 ms
6,944 KB |
| testcase_03 | AC | 1 ms
6,940 KB |
| testcase_04 | AC | 2 ms
6,940 KB |
| testcase_05 | AC | 2 ms
6,944 KB |
| testcase_06 | AC | 2 ms
6,940 KB |
| testcase_07 | AC | 2 ms
6,940 KB |
| testcase_08 | AC | 2 ms
6,940 KB |
| testcase_09 | AC | 2 ms
6,944 KB |
| testcase_10 | AC | 2 ms
6,940 KB |
| testcase_11 | AC | 2 ms
6,944 KB |
| testcase_12 | AC | 2 ms
6,944 KB |
| testcase_13 | AC | 2 ms
6,944 KB |
| testcase_14 | AC | 2 ms
6,940 KB |
| testcase_15 | AC | 2 ms
6,940 KB |
| testcase_16 | AC | 2 ms
6,944 KB |
| testcase_17 | AC | 2 ms
6,940 KB |
| testcase_18 | AC | 1 ms
6,940 KB |
| testcase_19 | AC | 2 ms
6,944 KB |
| testcase_20 | AC | 2 ms
6,940 KB |
ソースコード
#line 1 "main.cpp"
#include <bits/stdc++.h>
#line 1 "/home/anqooqie/.proconlib/tools/bigint.hpp"
#line 10 "/home/anqooqie/.proconlib/tools/bigint.hpp"
#include <type_traits>
#line 1 "/home/anqooqie/.proconlib/lib/ac-library/atcoder/modint.hpp"
#line 7 "/home/anqooqie/.proconlib/lib/ac-library/atcoder/modint.hpp"
#ifdef _MSC_VER
#include <intrin.h>
#endif
#line 1 "/home/anqooqie/.proconlib/lib/ac-library/atcoder/internal_math.hpp"
#line 5 "/home/anqooqie/.proconlib/lib/ac-library/atcoder/internal_math.hpp"
#ifdef _MSC_VER
#include <intrin.h>
#endif
namespace atcoder {
namespace internal {
// @param m `1 <= m`
// @return x mod m
constexpr long long safe_mod(long long x, long long m) {
x %= m;
if (x < 0) x += m;
return x;
}
// Fast modular multiplication by barrett reduction
// Reference: https://en.wikipedia.org/wiki/Barrett_reduction
// NOTE: reconsider after Ice Lake
struct barrett {
unsigned int _m;
unsigned long long im;
// @param m `1 <= m < 2^31`
explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}
// @return m
unsigned int umod() const { return _m; }
// @param a `0 <= a < m`
// @param b `0 <= b < m`
// @return `a * b % m`
unsigned int mul(unsigned int a, unsigned int b) const {
// [1] m = 1
// a = b = im = 0, so okay
// [2] m >= 2
// im = ceil(2^64 / m)
// -> im * m = 2^64 + r (0 <= r < m)
// let z = a*b = c*m + d (0 <= c, d < m)
// a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im
// c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) < 2^64 * 2
// ((ab * im) >> 64) == c or c + 1
unsigned long long z = a;
z *= b;
#ifdef _MSC_VER
unsigned long long x;
_umul128(z, im, &x);
#else
unsigned long long x =
(unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
unsigned int v = (unsigned int)(z - x * _m);
if (_m <= v) v += _m;
return v;
}
};
// @param n `0 <= n`
// @param m `1 <= m`
// @return `(x ** n) % m`
constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
if (m == 1) return 0;
unsigned int _m = (unsigned int)(m);
unsigned long long r = 1;
unsigned long long y = safe_mod(x, m);
while (n) {
if (n & 1) r = (r * y) % _m;
y = (y * y) % _m;
n >>= 1;
}
return r;
}
// Reference:
// M. Forisek and J. Jancina,
// Fast Primality Testing for Integers That Fit into a Machine Word
// @param n `0 <= n`
constexpr bool is_prime_constexpr(int n) {
if (n <= 1) return false;
if (n == 2 || n == 7 || n == 61) return true;
if (n % 2 == 0) return false;
long long d = n - 1;
while (d % 2 == 0) d /= 2;
constexpr long long bases[3] = {2, 7, 61};
for (long long a : bases) {
long long t = d;
long long y = pow_mod_constexpr(a, t, n);
while (t != n - 1 && y != 1 && y != n - 1) {
y = y * y % n;
t <<= 1;
}
if (y != n - 1 && t % 2 == 0) {
return false;
}
}
return true;
}
template <int n> constexpr bool is_prime = is_prime_constexpr(n);
// @param b `1 <= b`
// @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
a = safe_mod(a, b);
if (a == 0) return {b, 0};
// Contracts:
// [1] s - m0 * a = 0 (mod b)
// [2] t - m1 * a = 0 (mod b)
// [3] s * |m1| + t * |m0| <= b
long long s = b, t = a;
long long m0 = 0, m1 = 1;
while (t) {
long long u = s / t;
s -= t * u;
m0 -= m1 * u; // |m1 * u| <= |m1| * s <= b
// [3]:
// (s - t * u) * |m1| + t * |m0 - m1 * u|
// <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)
// = s * |m1| + t * |m0| <= b
auto tmp = s;
s = t;
t = tmp;
tmp = m0;
m0 = m1;
m1 = tmp;
}
// by [3]: |m0| <= b/g
// by g != b: |m0| < b/g
if (m0 < 0) m0 += b / s;
return {s, m0};
}
// Compile time primitive root
// @param m must be prime
// @return primitive root (and minimum in now)
constexpr int primitive_root_constexpr(int m) {
if (m == 2) return 1;
if (m == 167772161) return 3;
if (m == 469762049) return 3;
if (m == 754974721) return 11;
if (m == 998244353) return 3;
int divs[20] = {};
divs[0] = 2;
int cnt = 1;
int x = (m - 1) / 2;
while (x % 2 == 0) x /= 2;
for (int i = 3; (long long)(i)*i <= x; i += 2) {
if (x % i == 0) {
divs[cnt++] = i;
while (x % i == 0) {
x /= i;
}
}
}
if (x > 1) {
divs[cnt++] = x;
}
for (int g = 2;; g++) {
bool ok = true;
for (int i = 0; i < cnt; i++) {
if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
ok = false;
break;
}
}
if (ok) return g;
}
}
template <int m> constexpr int primitive_root = primitive_root_constexpr(m);
// @param n `n < 2^32`
// @param m `1 <= m < 2^32`
// @return sum_{i=0}^{n-1} floor((ai + b) / m) (mod 2^64)
unsigned long long floor_sum_unsigned(unsigned long long n,
unsigned long long m,
unsigned long long a,
unsigned long long b) {
unsigned long long ans = 0;
while (true) {
if (a >= m) {
ans += n * (n - 1) / 2 * (a / m);
a %= m;
}
if (b >= m) {
ans += n * (b / m);
b %= m;
}
unsigned long long y_max = a * n + b;
if (y_max < m) break;
// y_max < m * (n + 1)
// floor(y_max / m) <= n
n = (unsigned long long)(y_max / m);
b = (unsigned long long)(y_max % m);
std::swap(m, a);
}
return ans;
}
} // namespace internal
} // namespace atcoder
#line 1 "/home/anqooqie/.proconlib/lib/ac-library/atcoder/internal_type_traits.hpp"
#line 7 "/home/anqooqie/.proconlib/lib/ac-library/atcoder/internal_type_traits.hpp"
namespace atcoder {
namespace internal {
#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value ||
std::is_same<T, __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int128 =
typename std::conditional<std::is_same<T, __uint128_t>::value ||
std::is_same<T, unsigned __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using make_unsigned_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value,
__uint128_t,
unsigned __int128>;
template <class T>
using is_integral = typename std::conditional<std::is_integral<T>::value ||
is_signed_int128<T>::value ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value &&
std::is_signed<T>::value) ||
is_signed_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<(is_integral<T>::value &&
std::is_unsigned<T>::value) ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<
is_signed_int128<T>::value,
make_unsigned_int128<T>,
typename std::conditional<std::is_signed<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type>::type;
#else
template <class T> using is_integral = typename std::is_integral<T>;
template <class T>
using is_signed_int =
typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<is_integral<T>::value &&
std::is_unsigned<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<is_signed_int<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type;
#endif
template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;
template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;
template <class T> using to_unsigned_t = typename to_unsigned<T>::type;
} // namespace internal
} // namespace atcoder
#line 14 "/home/anqooqie/.proconlib/lib/ac-library/atcoder/modint.hpp"
namespace atcoder {
namespace internal {
struct modint_base {};
struct static_modint_base : modint_base {};
template <class T> using is_modint = std::is_base_of<modint_base, T>;
template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;
} // namespace internal
template <int m, std::enable_if_t<(1 <= m)>* = nullptr>
struct static_modint : internal::static_modint_base {
using mint = static_modint;
public:
static constexpr int mod() { return m; }
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
static_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T>* = nullptr>
static_modint(T v) {
long long x = (long long)(v % (long long)(umod()));
if (x < 0) x += umod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T>* = nullptr>
static_modint(T v) {
_v = (unsigned int)(v % umod());
}
unsigned int val() const { return _v; }
mint& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
mint& operator+=(const mint& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator-=(const mint& rhs) {
_v -= rhs._v;
if (_v >= umod()) _v += umod();
return *this;
}
mint& operator*=(const mint& rhs) {
unsigned long long z = _v;
z *= rhs._v;
_v = (unsigned int)(z % umod());
return *this;
}
mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const {
if (prime) {
assert(_v);
return pow(umod() - 2);
} else {
auto eg = internal::inv_gcd(_v, m);
assert(eg.first == 1);
return eg.second;
}
}
friend mint operator+(const mint& lhs, const mint& rhs) {
return mint(lhs) += rhs;
}
friend mint operator-(const mint& lhs, const mint& rhs) {
return mint(lhs) -= rhs;
}
friend mint operator*(const mint& lhs, const mint& rhs) {
return mint(lhs) *= rhs;
}
friend mint operator/(const mint& lhs, const mint& rhs) {
return mint(lhs) /= rhs;
}
friend bool operator==(const mint& lhs, const mint& rhs) {
return lhs._v == rhs._v;
}
friend bool operator!=(const mint& lhs, const mint& rhs) {
return lhs._v != rhs._v;
}
private:
unsigned int _v;
static constexpr unsigned int umod() { return m; }
static constexpr bool prime = internal::is_prime<m>;
};
template <int id> struct dynamic_modint : internal::modint_base {
using mint = dynamic_modint;
public:
static int mod() { return (int)(bt.umod()); }
static void set_mod(int m) {
assert(1 <= m);
bt = internal::barrett(m);
}
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
dynamic_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T>* = nullptr>
dynamic_modint(T v) {
long long x = (long long)(v % (long long)(mod()));
if (x < 0) x += mod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T>* = nullptr>
dynamic_modint(T v) {
_v = (unsigned int)(v % mod());
}
unsigned int val() const { return _v; }
mint& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
mint& operator+=(const mint& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator-=(const mint& rhs) {
_v += mod() - rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator*=(const mint& rhs) {
_v = bt.mul(_v, rhs._v);
return *this;
}
mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const {
auto eg = internal::inv_gcd(_v, mod());
assert(eg.first == 1);
return eg.second;
}
friend mint operator+(const mint& lhs, const mint& rhs) {
return mint(lhs) += rhs;
}
friend mint operator-(const mint& lhs, const mint& rhs) {
return mint(lhs) -= rhs;
}
friend mint operator*(const mint& lhs, const mint& rhs) {
return mint(lhs) *= rhs;
}
friend mint operator/(const mint& lhs, const mint& rhs) {
return mint(lhs) /= rhs;
}
friend bool operator==(const mint& lhs, const mint& rhs) {
return lhs._v == rhs._v;
}
friend bool operator!=(const mint& lhs, const mint& rhs) {
return lhs._v != rhs._v;
}
private:
unsigned int _v;
static internal::barrett bt;
static unsigned int umod() { return bt.umod(); }
};
template <int id> internal::barrett dynamic_modint<id>::bt(998244353);
using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;
namespace internal {
template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base, T>;
template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;
template <class> struct is_dynamic_modint : public std::false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};
template <class T>
using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;
} // namespace internal
} // namespace atcoder
#line 1 "/home/anqooqie/.proconlib/lib/ac-library/atcoder/convolution.hpp"
#line 9 "/home/anqooqie/.proconlib/lib/ac-library/atcoder/convolution.hpp"
#line 1 "/home/anqooqie/.proconlib/lib/ac-library/atcoder/internal_bit.hpp"
#ifdef _MSC_VER
#include <intrin.h>
#endif
namespace atcoder {
namespace internal {
// @param n `0 <= n`
// @return minimum non-negative `x` s.t. `n <= 2**x`
int ceil_pow2(int n) {
int x = 0;
while ((1U << x) < (unsigned int)(n)) x++;
return x;
}
// @param n `1 <= n`
// @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0`
constexpr int bsf_constexpr(unsigned int n) {
int x = 0;
while (!(n & (1 << x))) x++;
return x;
}
// @param n `1 <= n`
// @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0`
int bsf(unsigned int n) {
#ifdef _MSC_VER
unsigned long index;
_BitScanForward(&index, n);
return index;
#else
return __builtin_ctz(n);
#endif
}
} // namespace internal
} // namespace atcoder
#line 12 "/home/anqooqie/.proconlib/lib/ac-library/atcoder/convolution.hpp"
namespace atcoder {
namespace internal {
template <class mint,
int g = internal::primitive_root<mint::mod()>,
internal::is_static_modint_t<mint>* = nullptr>
struct fft_info {
static constexpr int rank2 = bsf_constexpr(mint::mod() - 1);
std::array<mint, rank2 + 1> root; // root[i]^(2^i) == 1
std::array<mint, rank2 + 1> iroot; // root[i] * iroot[i] == 1
std::array<mint, std::max(0, rank2 - 2 + 1)> rate2;
std::array<mint, std::max(0, rank2 - 2 + 1)> irate2;
std::array<mint, std::max(0, rank2 - 3 + 1)> rate3;
std::array<mint, std::max(0, rank2 - 3 + 1)> irate3;
fft_info() {
root[rank2] = mint(g).pow((mint::mod() - 1) >> rank2);
iroot[rank2] = root[rank2].inv();
for (int i = rank2 - 1; i >= 0; i--) {
root[i] = root[i + 1] * root[i + 1];
iroot[i] = iroot[i + 1] * iroot[i + 1];
}
{
mint prod = 1, iprod = 1;
for (int i = 0; i <= rank2 - 2; i++) {
rate2[i] = root[i + 2] * prod;
irate2[i] = iroot[i + 2] * iprod;
prod *= iroot[i + 2];
iprod *= root[i + 2];
}
}
{
mint prod = 1, iprod = 1;
for (int i = 0; i <= rank2 - 3; i++) {
rate3[i] = root[i + 3] * prod;
irate3[i] = iroot[i + 3] * iprod;
prod *= iroot[i + 3];
iprod *= root[i + 3];
}
}
}
};
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
void butterfly(std::vector<mint>& a) {
int n = int(a.size());
int h = internal::ceil_pow2(n);
static const fft_info<mint> info;
int len = 0; // a[i, i+(n>>len), i+2*(n>>len), ..] is transformed
while (len < h) {
if (h - len == 1) {
int p = 1 << (h - len - 1);
mint rot = 1;
for (int s = 0; s < (1 << len); s++) {
int offset = s << (h - len);
for (int i = 0; i < p; i++) {
auto l = a[i + offset];
auto r = a[i + offset + p] * rot;
a[i + offset] = l + r;
a[i + offset + p] = l - r;
}
if (s + 1 != (1 << len))
rot *= info.rate2[bsf(~(unsigned int)(s))];
}
len++;
} else {
// 4-base
int p = 1 << (h - len - 2);
mint rot = 1, imag = info.root[2];
for (int s = 0; s < (1 << len); s++) {
mint rot2 = rot * rot;
mint rot3 = rot2 * rot;
int offset = s << (h - len);
for (int i = 0; i < p; i++) {
auto mod2 = 1ULL * mint::mod() * mint::mod();
auto a0 = 1ULL * a[i + offset].val();
auto a1 = 1ULL * a[i + offset + p].val() * rot.val();
auto a2 = 1ULL * a[i + offset + 2 * p].val() * rot2.val();
auto a3 = 1ULL * a[i + offset + 3 * p].val() * rot3.val();
auto a1na3imag =
1ULL * mint(a1 + mod2 - a3).val() * imag.val();
auto na2 = mod2 - a2;
a[i + offset] = a0 + a2 + a1 + a3;
a[i + offset + 1 * p] = a0 + a2 + (2 * mod2 - (a1 + a3));
a[i + offset + 2 * p] = a0 + na2 + a1na3imag;
a[i + offset + 3 * p] = a0 + na2 + (mod2 - a1na3imag);
}
if (s + 1 != (1 << len))
rot *= info.rate3[bsf(~(unsigned int)(s))];
}
len += 2;
}
}
}
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
void butterfly_inv(std::vector<mint>& a) {
int n = int(a.size());
int h = internal::ceil_pow2(n);
static const fft_info<mint> info;
int len = h; // a[i, i+(n>>len), i+2*(n>>len), ..] is transformed
while (len) {
if (len == 1) {
int p = 1 << (h - len);
mint irot = 1;
for (int s = 0; s < (1 << (len - 1)); s++) {
int offset = s << (h - len + 1);
for (int i = 0; i < p; i++) {
auto l = a[i + offset];
auto r = a[i + offset + p];
a[i + offset] = l + r;
a[i + offset + p] =
(unsigned long long)(mint::mod() + l.val() - r.val()) *
irot.val();
;
}
if (s + 1 != (1 << (len - 1)))
irot *= info.irate2[bsf(~(unsigned int)(s))];
}
len--;
} else {
// 4-base
int p = 1 << (h - len);
mint irot = 1, iimag = info.iroot[2];
for (int s = 0; s < (1 << (len - 2)); s++) {
mint irot2 = irot * irot;
mint irot3 = irot2 * irot;
int offset = s << (h - len + 2);
for (int i = 0; i < p; i++) {
auto a0 = 1ULL * a[i + offset + 0 * p].val();
auto a1 = 1ULL * a[i + offset + 1 * p].val();
auto a2 = 1ULL * a[i + offset + 2 * p].val();
auto a3 = 1ULL * a[i + offset + 3 * p].val();
auto a2na3iimag =
1ULL *
mint((mint::mod() + a2 - a3) * iimag.val()).val();
a[i + offset] = a0 + a1 + a2 + a3;
a[i + offset + 1 * p] =
(a0 + (mint::mod() - a1) + a2na3iimag) * irot.val();
a[i + offset + 2 * p] =
(a0 + a1 + (mint::mod() - a2) + (mint::mod() - a3)) *
irot2.val();
a[i + offset + 3 * p] =
(a0 + (mint::mod() - a1) + (mint::mod() - a2na3iimag)) *
irot3.val();
}
if (s + 1 != (1 << (len - 2)))
irot *= info.irate3[bsf(~(unsigned int)(s))];
}
len -= 2;
}
}
}
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
std::vector<mint> convolution_naive(const std::vector<mint>& a,
const std::vector<mint>& b) {
int n = int(a.size()), m = int(b.size());
std::vector<mint> ans(n + m - 1);
if (n < m) {
for (int j = 0; j < m; j++) {
for (int i = 0; i < n; i++) {
ans[i + j] += a[i] * b[j];
}
}
} else {
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
ans[i + j] += a[i] * b[j];
}
}
}
return ans;
}
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
std::vector<mint> convolution_fft(std::vector<mint> a, std::vector<mint> b) {
int n = int(a.size()), m = int(b.size());
int z = 1 << internal::ceil_pow2(n + m - 1);
a.resize(z);
internal::butterfly(a);
b.resize(z);
internal::butterfly(b);
for (int i = 0; i < z; i++) {
a[i] *= b[i];
}
internal::butterfly_inv(a);
a.resize(n + m - 1);
mint iz = mint(z).inv();
for (int i = 0; i < n + m - 1; i++) a[i] *= iz;
return a;
}
} // namespace internal
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
std::vector<mint> convolution(std::vector<mint>&& a, std::vector<mint>&& b) {
int n = int(a.size()), m = int(b.size());
if (!n || !m) return {};
if (std::min(n, m) <= 60) return convolution_naive(a, b);
return internal::convolution_fft(a, b);
}
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
std::vector<mint> convolution(const std::vector<mint>& a,
const std::vector<mint>& b) {
int n = int(a.size()), m = int(b.size());
if (!n || !m) return {};
if (std::min(n, m) <= 60) return convolution_naive(a, b);
return internal::convolution_fft(a, b);
}
template <unsigned int mod = 998244353,
class T,
std::enable_if_t<internal::is_integral<T>::value>* = nullptr>
std::vector<T> convolution(const std::vector<T>& a, const std::vector<T>& b) {
int n = int(a.size()), m = int(b.size());
if (!n || !m) return {};
using mint = static_modint<mod>;
std::vector<mint> a2(n), b2(m);
for (int i = 0; i < n; i++) {
a2[i] = mint(a[i]);
}
for (int i = 0; i < m; i++) {
b2[i] = mint(b[i]);
}
auto c2 = convolution(move(a2), move(b2));
std::vector<T> c(n + m - 1);
for (int i = 0; i < n + m - 1; i++) {
c[i] = c2[i].val();
}
return c;
}
std::vector<long long> convolution_ll(const std::vector<long long>& a,
const std::vector<long long>& b) {
int n = int(a.size()), m = int(b.size());
if (!n || !m) return {};
static constexpr unsigned long long MOD1 = 754974721; // 2^24
static constexpr unsigned long long MOD2 = 167772161; // 2^25
static constexpr unsigned long long MOD3 = 469762049; // 2^26
static constexpr unsigned long long M2M3 = MOD2 * MOD3;
static constexpr unsigned long long M1M3 = MOD1 * MOD3;
static constexpr unsigned long long M1M2 = MOD1 * MOD2;
static constexpr unsigned long long M1M2M3 = MOD1 * MOD2 * MOD3;
static constexpr unsigned long long i1 =
internal::inv_gcd(MOD2 * MOD3, MOD1).second;
static constexpr unsigned long long i2 =
internal::inv_gcd(MOD1 * MOD3, MOD2).second;
static constexpr unsigned long long i3 =
internal::inv_gcd(MOD1 * MOD2, MOD3).second;
auto c1 = convolution<MOD1>(a, b);
auto c2 = convolution<MOD2>(a, b);
auto c3 = convolution<MOD3>(a, b);
std::vector<long long> c(n + m - 1);
for (int i = 0; i < n + m - 1; i++) {
unsigned long long x = 0;
x += (c1[i] * i1) % MOD1 * M2M3;
x += (c2[i] * i2) % MOD2 * M1M3;
x += (c3[i] * i3) % MOD3 * M1M2;
// B = 2^63, -B <= x, r(real value) < B
// (x, x - M, x - 2M, or x - 3M) = r (mod 2B)
// r = c1[i] (mod MOD1)
// focus on MOD1
// r = x, x - M', x - 2M', x - 3M' (M' = M % 2^64) (mod 2B)
// r = x,
// x - M' + (0 or 2B),
// x - 2M' + (0, 2B or 4B),
// x - 3M' + (0, 2B, 4B or 6B) (without mod!)
// (r - x) = 0, (0)
// - M' + (0 or 2B), (1)
// -2M' + (0 or 2B or 4B), (2)
// -3M' + (0 or 2B or 4B or 6B) (3) (mod MOD1)
// we checked that
// ((1) mod MOD1) mod 5 = 2
// ((2) mod MOD1) mod 5 = 3
// ((3) mod MOD1) mod 5 = 4
long long diff =
c1[i] - internal::safe_mod((long long)(x), (long long)(MOD1));
if (diff < 0) diff += MOD1;
static constexpr unsigned long long offset[5] = {
0, 0, M1M2M3, 2 * M1M2M3, 3 * M1M2M3};
x -= offset[diff % 5];
c[i] = x;
}
return c;
}
} // namespace atcoder
#line 1 "/home/anqooqie/.proconlib/tools/quo.hpp"
#line 5 "/home/anqooqie/.proconlib/tools/quo.hpp"
namespace tools {
template <typename M, typename N>
constexpr ::std::common_type_t<M, N> quo(const M lhs, const N rhs) {
if (lhs >= 0) {
return lhs / rhs;
} else {
if (rhs >= 0) {
return -((-lhs - 1 + rhs) / rhs);
} else {
return (-lhs - 1 + -rhs) / -rhs;
}
}
}
}
#line 1 "/home/anqooqie/.proconlib/tools/mod.hpp"
#line 6 "/home/anqooqie/.proconlib/tools/mod.hpp"
namespace tools {
template <typename M, typename N>
constexpr ::std::common_type_t<M, N> mod(const M lhs, const N rhs) {
if constexpr (::std::is_unsigned_v<M> && ::std::is_unsigned_v<N>) {
return lhs % rhs;
} else {
return lhs - ::tools::quo(lhs, rhs) * rhs;
}
}
}
#line 1 "/home/anqooqie/.proconlib/tools/floor.hpp"
#line 6 "/home/anqooqie/.proconlib/tools/floor.hpp"
namespace tools {
template <typename M, typename N>
constexpr ::std::common_type_t<M, N> floor(const M lhs, const N rhs) {
assert(rhs != 0);
return lhs / rhs - (((lhs > 0 && rhs < 0) || (lhs < 0 && rhs > 0)) && lhs % rhs);
}
}
#line 1 "/home/anqooqie/.proconlib/tools/ssize.hpp"
#line 6 "/home/anqooqie/.proconlib/tools/ssize.hpp"
namespace tools {
template <typename C>
constexpr auto ssize(const C& c) -> ::std::common_type_t<::std::ptrdiff_t, ::std::make_signed_t<decltype(c.size())>> {
return c.size();
}
}
#line 1 "/home/anqooqie/.proconlib/tools/ceil.hpp"
#line 6 "/home/anqooqie/.proconlib/tools/ceil.hpp"
namespace tools {
template <typename M, typename N>
constexpr ::std::common_type_t<M, N> ceil(const M lhs, const N rhs) {
assert(rhs != 0);
return lhs / rhs + (((lhs > 0 && rhs > 0) || (lhs < 0 && rhs < 0)) && lhs % rhs);
}
}
#line 1 "/home/anqooqie/.proconlib/tools/garner2.hpp"
#line 1 "/home/anqooqie/.proconlib/tools/is_prime.hpp"
#line 1 "/home/anqooqie/.proconlib/tools/prod_mod.hpp"
namespace tools {
template <typename T1, typename T2, typename T3>
constexpr T3 prod_mod(const T1 x, const T2 y, const T3 m) {
using u128 = unsigned __int128;
u128 prod_mod = u128(x >= 0 ? x : -x) * u128(y >= 0 ? y : -y) % u128(m);
if ((x >= 0) ^ (y >= 0)) prod_mod = u128(m) - prod_mod;
return prod_mod;
}
}
#line 1 "/home/anqooqie/.proconlib/tools/pow_mod.hpp"
#line 6 "/home/anqooqie/.proconlib/tools/pow_mod.hpp"
namespace tools {
template <typename T1, typename T2, typename T3>
constexpr T3 pow_mod(const T1 x, T2 n, const T3 m) {
if (m == 1) return 0;
T3 r = 1;
T3 y = ::tools::mod(x, m);
while (n > 0) {
if ((n & 1) > 0) {
r = ::tools::prod_mod(r, y, m);
}
y = ::tools::prod_mod(y, y, m);
n /= 2;
}
return r;
}
}
#line 7 "/home/anqooqie/.proconlib/tools/is_prime.hpp"
namespace tools {
constexpr bool is_prime(const ::std::uint_fast64_t n) {
constexpr ::std::array<unsigned long long, 7> bases = {2, 325, 9375, 28178, 450775, 9780504, 1795265022};
if (n <= 1) return false;
if (n == 2) return true;
if (n % 2 == 0) return false;
auto d = n - 1;
for (; d % 2 == 0; d /= 2);
for (const auto a : bases) {
if (a % n == 0) return true;
auto power = d;
auto target = ::tools::pow_mod(a, power, n);
bool is_composite = true;
if (target == 1) is_composite = false;
for (; is_composite && power != n - 1; power *= 2, target = ::tools::prod_mod(target, target, n)) {
if (target == n - 1) is_composite = false;
}
if (is_composite) {
return false;
}
}
return true;
}
}
#line 6 "/home/anqooqie/.proconlib/tools/garner2.hpp"
namespace tools {
template <typename M1, typename M2>
long long garner2(const M1& a, const M2& b) {
using ull = unsigned long long;
static constexpr ull m1_m2 = ull(M1::mod()) * ull(M2::mod());
static const M2 m1_inv_mod_m2 = M2::raw(M1::mod()).inv();
assert(M1::mod() < M2::mod());
assert(::tools::is_prime(M1::mod()));
assert(::tools::is_prime(M2::mod()));
// t = (b - a) / M1; (mod M2)
// return a + t * M1;
const M2 t = (b - M2::raw(a.val())) * m1_inv_mod_m2;
ull r = t.val();
r *= M1::mod();
r += a.val();
if (r >= m1_m2) r -= m1_m2;
return r;
}
}
#line 1 "/home/anqooqie/.proconlib/tools/pow2.hpp"
#line 6 "/home/anqooqie/.proconlib/tools/pow2.hpp"
namespace tools {
template <typename T, typename ::std::enable_if<::std::is_unsigned<T>::value, ::std::nullptr_t>::type = nullptr>
constexpr T pow2(const T x) {
return static_cast<T>(1) << x;
}
template <typename T, typename ::std::enable_if<::std::is_signed<T>::value, ::std::nullptr_t>::type = nullptr>
constexpr T pow2(const T x) {
return static_cast<T>(static_cast<typename ::std::make_unsigned<T>::type>(1) << static_cast<typename ::std::make_unsigned<T>::type>(x));
}
}
#line 1 "/home/anqooqie/.proconlib/tools/abs.hpp"
namespace tools {
constexpr float abs(const float x) {
return x < 0 ? -x : x;
}
constexpr double abs(const double x) {
return x < 0 ? -x : x;
}
constexpr long double abs(const long double x) {
return x < 0 ? -x : x;
}
constexpr int abs(const int x) {
return x < 0 ? -x : x;
}
constexpr long abs(const long x) {
return x < 0 ? -x : x;
}
constexpr long long abs(const long long x) {
return x < 0 ? -x : x;
}
}
#line 1 "/home/anqooqie/.proconlib/tools/gcd.hpp"
#line 6 "/home/anqooqie/.proconlib/tools/gcd.hpp"
namespace tools {
template <typename M, typename N>
constexpr ::std::common_type_t<M, N> gcd(const M m, const N n) {
return ::std::gcd(m, n);
}
}
#line 29 "/home/anqooqie/.proconlib/tools/bigint.hpp"
namespace tools {
class bigint {
private:
using mint1 = ::atcoder::static_modint<167772161>;
using mint2 = ::atcoder::static_modint<469762049>;
bool m_positive;
::std::vector<::std::int_fast32_t> m_digits;
static constexpr ::std::int_fast32_t BASE = 10000;
static constexpr ::std::int_fast32_t LOG10_BASE = 4;
static constexpr ::std::array<::std::int_fast32_t, 5> POW10 = {1, 10, 100, 1000, 10000};
static int compare_3way(const ::std::size_t lhs, const ::std::size_t rhs) {
if (lhs < rhs) return -1;
if (lhs == rhs) return 0;
return 1;
}
static int compare_3way_abs(const ::tools::bigint& lhs, const ::tools::bigint& rhs) {
if (const auto comp = ::tools::bigint::compare_3way(lhs.m_digits.size(), rhs.m_digits.size()); comp != 0) {
return comp;
}
for (::std::size_t i = 0; i < lhs.m_digits.size(); ++i) {
if (const auto comp = ::tools::bigint::compare_3way(lhs.m_digits[lhs.m_digits.size() - 1 - i], rhs.m_digits[rhs.m_digits.size() - 1 - i]); comp != 0) {
return comp;
}
}
return 0;
}
::tools::bigint& regularize(const int level) {
if (level > 0) {
if (level == 2) {
for (::std::size_t i = 0; i + 1 < this->m_digits.size(); ++i) {
this->m_digits[i + 1] += ::tools::quo(this->m_digits[i], BASE);
this->m_digits[i] = ::tools::mod(this->m_digits[i], BASE);
}
} else {
for (::std::size_t i = 0; i + 1 < this->m_digits.size(); ++i) {
if (this->m_digits[i] < 0) {
this->m_digits[i] += BASE;
--this->m_digits[i + 1];
} else if (this->m_digits[i] >= BASE) {
this->m_digits[i] -= BASE;
++this->m_digits[i + 1];
}
}
}
if (!this->m_digits.empty() && this->m_digits.back() < 0) {
this->m_positive = !this->m_positive;
for (::std::size_t i = 0; i < this->m_digits.size(); ++i) {
this->m_digits[i] = -this->m_digits[i];
}
for (::std::size_t i = 0; i + 1 < this->m_digits.size(); ++i) {
if (this->m_digits[i] < 0) {
this->m_digits[i] = BASE + this->m_digits[i];
--this->m_digits[i + 1];
}
}
}
if (level == 2) {
while (!this->m_digits.empty() && this->m_digits.back() >= BASE) {
this->m_digits.push_back(this->m_digits.back() / BASE);
this->m_digits[this->m_digits.size() - 2] %= BASE;
}
} else {
if (!this->m_digits.empty() && this->m_digits.back() >= BASE) {
this->m_digits.back() -= BASE;
this->m_digits.push_back(1);
}
}
}
while (!this->m_digits.empty() && this->m_digits.back() == 0) {
this->m_digits.pop_back();
}
if (this->m_digits.empty() && !this->m_positive) {
this->m_positive = true;
}
return *this;
}
public:
::tools::bigint& negate() {
if (!this->m_digits.empty()) {
this->m_positive = !this->m_positive;
}
return *this;
}
::tools::bigint& multiply_by_pow10(const ::std::ptrdiff_t exponent) {
if (!this->m_digits.empty()) {
const ::std::ptrdiff_t exponent10000 = ::tools::floor(exponent, LOG10_BASE);
::std::int_fast32_t mod = 0;
if (exponent10000 > 0) {
::std::vector<::std::int_fast32_t> zero(exponent10000, 0);
this->m_digits.insert(this->m_digits.begin(), zero.begin(), zero.end());
} else if (exponent10000 < 0) {
if (::tools::ssize(this->m_digits) >= -exponent10000) {
mod = this->m_digits[-exponent10000 - 1] / POW10[LOG10_BASE * (exponent10000 + 1) - exponent];
}
this->m_digits.erase(this->m_digits.begin(), this->m_digits.begin() + ::std::min<::std::size_t>(-exponent10000, this->m_digits.size()));
}
if (const ::std::int_fast32_t coefficient = POW10[exponent - LOG10_BASE * exponent10000]; coefficient > POW10[0]) {
for (auto& d : this->m_digits) {
d *= coefficient;
}
if (mod > 0 && this->m_digits.empty()) {
this->m_digits.push_back(0);
}
this->m_digits[0] += mod;
this->regularize(2);
} else {
this->regularize(0);
}
}
return *this;
}
::tools::bigint& divide_by_pow10(const ::std::ptrdiff_t exponent) {
this->multiply_by_pow10(-exponent);
return *this;
}
static int compare_3way(const ::tools::bigint& lhs, const ::tools::bigint& rhs) {
if (!lhs.m_positive && rhs.m_positive) return -1;
if (lhs.m_positive && !rhs.m_positive) return 1;
return ::tools::bigint::compare_3way_abs(lhs, rhs) * (lhs.m_positive ? 1 : -1);
}
int signum() const {
if (!this->m_positive) return -1;
if (this->m_digits.empty()) return 0;
return 1;
}
::std::size_t size() const {
if (this->m_digits.empty()) return 0;
return LOG10_BASE * (this->m_digits.size() - 1) + ::std::distance(POW10.begin(), ::std::upper_bound(POW10.begin(), POW10.end(), this->m_digits[this->m_digits.size() - 1]));
}
::std::int_fast32_t operator[](const ::std::size_t i) const {
return i < LOG10_BASE * this->m_digits.size() ? this->m_digits[i / LOG10_BASE] / POW10[i % LOG10_BASE] % 10 : 0;
}
private:
::tools::bigint& internal_add(const ::tools::bigint& other, const bool plus) {
const bool this_positive = this->m_positive;
if (!this_positive) {
this->negate();
}
this->m_digits.resize(::std::max(this->m_digits.size(), other.m_digits.size()));
if (this_positive == (other.m_positive == plus)) {
for (::std::size_t i = 0; i < other.m_digits.size(); ++i) {
this->m_digits[i] += other.m_digits[i];
}
} else {
for (::std::size_t i = 0; i < other.m_digits.size(); ++i) {
this->m_digits[i] -= other.m_digits[i];
}
}
this->regularize(1);
if (!this_positive) {
this->negate();
}
return *this;
}
public:
bigint() : m_positive(true) {
}
bigint(const ::tools::bigint&) = default;
bigint(::tools::bigint&&) = default;
~bigint() = default;
::tools::bigint& operator=(const ::tools::bigint&) = default;
::tools::bigint& operator=(::tools::bigint&&) = default;
template <typename T, typename ::std::enable_if<::std::is_integral_v<T>, ::std::nullptr_t>::type = nullptr>
explicit bigint(T n) : m_positive(n >= 0) {
while (n != 0) {
this->m_digits.push_back(n % BASE);
n /= BASE;
}
if (!this->m_positive) {
for (auto& d : this->m_digits) {
d = -d;
}
}
}
explicit bigint(const ::std::string& s) {
assert(!s.empty());
::std::size_t offset;
if (s[0] == '+') {
this->m_positive = true;
offset = 1;
} else if (s[0] == '-') {
this->m_positive = false;
offset = 1;
} else {
this->m_positive = true;
offset = 0;
}
this->m_digits.reserve(::tools::ceil<::std::size_t>(s.size() - offset, LOG10_BASE));
for (::std::size_t i = 0; i < s.size() - offset; i += LOG10_BASE) {
this->m_digits.push_back(0);
for (::std::size_t j = ::std::min(i + LOG10_BASE, s.size() - offset); j --> i;) {
assert('0' <= s[s.size() - 1 - j] && s[s.size() - 1 - j] <= '9');
this->m_digits.back() = this->m_digits.back() * 10 + (s[s.size() - 1 - j] - '0');
}
}
this->regularize(0);
}
friend bool operator==(const ::tools::bigint& lhs, const ::tools::bigint& rhs) {
return lhs.m_positive == rhs.m_positive && lhs.m_digits == rhs.m_digits;
}
friend bool operator!=(const ::tools::bigint& lhs, const ::tools::bigint& rhs) {
return !(lhs == rhs);
}
friend bool operator<(const ::tools::bigint& lhs, const ::tools::bigint& rhs) {
return ::tools::bigint::compare_3way(lhs, rhs) < 0;
}
friend bool operator>(const ::tools::bigint& lhs, const ::tools::bigint& rhs) {
return ::tools::bigint::compare_3way(lhs, rhs) > 0;
}
friend bool operator<=(const ::tools::bigint& lhs, const ::tools::bigint& rhs) {
return ::tools::bigint::compare_3way(lhs, rhs) <= 0;
}
friend bool operator>=(const ::tools::bigint& lhs, const ::tools::bigint& rhs) {
return ::tools::bigint::compare_3way(lhs, rhs) >= 0;
}
::tools::bigint operator+() const {
return *this;
}
::tools::bigint operator-() const {
return ::tools::bigint(*this).negate();
}
::tools::bigint& operator+=(const ::tools::bigint& other) {
return this->internal_add(other, true);
}
::tools::bigint& operator-=(const ::tools::bigint& other) {
return this->internal_add(other, false);
}
::tools::bigint& operator*=(const ::tools::bigint& other) {
// Constraint derived from atcoder::convolution
assert(this->m_digits.size() + other.m_digits.size() <= ::tools::pow2(25) + 1);
::std::vector<mint1> a1, b1;
::std::vector<mint2> a2, b2;
a1.reserve(this->m_digits.size());
a2.reserve(this->m_digits.size());
b1.reserve(other.m_digits.size());
b2.reserve(other.m_digits.size());
for (const auto a_i : this->m_digits) {
a1.push_back(mint1::raw(a_i));
a2.push_back(mint2::raw(a_i));
}
for (const auto b_i : other.m_digits) {
b1.push_back(mint1::raw(b_i));
b2.push_back(mint2::raw(b_i));
}
const auto c1 = ::atcoder::convolution(a1, b1);
const auto c2 = ::atcoder::convolution(a2, b2);
this->m_digits.clear();
this->m_digits.reserve(c1.size() + 1);
long long carry = 0;
for (::std::size_t i = 0; i < c1.size(); ++i) {
// Since a_i <= 10^4 - 1 and b_i <= 10^4 - 1, c_i <= (10^4 - 1)^2 * min(this->m_digits.size(), other.m_digits.size()) holds.
// In addition, since this->m_digits.size() + other.m_digits.size() <= 2^25 + 1, c_i <= (10^4 - 1)^2 * 2^24 = 1677386072457216 holds eventually.
// 1677386072457216 < 167772161 * 469762049 = 78812994116517889 holds, so we can reconstruct c_i from mod(c_i, 167772161) and mod(c_i, 469762049) by CRT.
long long c_i = ::tools::garner2(c1[i], c2[i]);
c_i += carry;
carry = c_i / BASE;
c_i %= BASE;
this->m_digits.push_back(c_i);
}
if (carry > 0) {
this->m_digits.push_back(carry);
}
this->m_positive = this->m_positive == other.m_positive;
this->regularize(0);
return *this;
}
friend ::tools::bigint operator+(const ::tools::bigint& lhs, const ::tools::bigint& rhs) {
return ::tools::bigint(lhs) += rhs;
}
friend ::tools::bigint operator-(const ::tools::bigint& lhs, const ::tools::bigint& rhs) {
return ::tools::bigint(lhs) -= rhs;
}
friend ::tools::bigint operator*(const ::tools::bigint& lhs, const ::tools::bigint& rhs) {
return ::tools::bigint(lhs) *= rhs;
}
::tools::bigint& operator++() {
return *this += ::tools::bigint(1);
}
::tools::bigint operator++(int) {
::tools::bigint old(*this);
++(*this);
return old;
}
::tools::bigint& operator--() {
return *this -= ::tools::bigint(1);
}
::tools::bigint operator--(int) {
::tools::bigint old(*this);
--(*this);
return old;
}
::tools::bigint& operator/=(const ::tools::bigint& other) {
assert(other.signum() != 0);
if (::tools::bigint::compare_3way_abs(*this, other) < 0) {
this->m_digits.clear();
this->m_positive = true;
return *this;
}
if (other.m_digits.size() == 1 && other.m_digits[0] == 1) {
this->m_positive = (this->m_positive == other.m_positive);
return *this;
}
using u64 = ::std::uint_fast64_t;
static const ::tools::bigint u64_threshold((::std::numeric_limits<u64>::max() - (BASE - 1)) / BASE);
using u128 = unsigned __int128;
static const ::tools::bigint u128_threshold("34028236692093846346337460743176820");
#define TOOLS_BIGINT_NAIVE(type) do {\
if (::tools::bigint::compare_3way_abs(other, type ## _threshold) <= 0) { \
type mod = 0;\
for (::std::size_t i = other.m_digits.size(); i --> 0;) {\
mod *= BASE;\
mod += other.m_digits[i];\
}\
\
type carry = 0;\
for (::std::size_t i = this->m_digits.size(); i--> 0;) {\
carry *= BASE;\
carry += this->m_digits[i];\
this->m_digits[i] = carry / mod;\
carry %= mod;\
}\
\
this->m_positive = (this->m_positive == other.m_positive);\
return this->regularize(0);\
}\
} while (false)
TOOLS_BIGINT_NAIVE(u64);
TOOLS_BIGINT_NAIVE(u128);
#undef TOOLS_BIGINT_NAIVE
using bigdecimal = ::std::pair<::tools::bigint, ::std::ptrdiff_t>;
static const auto precision = [](const bigdecimal& x) {
return x.first.m_digits.size();
};
static const auto regularize = [](bigdecimal& x) -> bigdecimal& {
if (x.first.m_digits.empty()) {
x.second = 0;
}
return x;
};
static const auto negate = [](bigdecimal& x) -> bigdecimal& {
x.first.negate();
return x;
};
static const auto make_abs = [](bigdecimal& x) -> bigdecimal& {
if (!x.first.m_positive) {
negate(x);
}
return x;
};
static const auto set_precision = [](bigdecimal& x, const ::std::size_t p) -> bigdecimal& {
const ::std::ptrdiff_t diff = ::std::ptrdiff_t(p) - ::std::ptrdiff_t(precision(x));
x.first.multiply_by_pow10(diff * LOG10_BASE);
x.second -= diff;
regularize(x);
return x;
};
static const auto plus = [](bigdecimal& x, bigdecimal& y) -> bigdecimal& {
if (x.second < y.second) {
set_precision(y, precision(y) + (y.second - x.second));
} else if (x.second > y.second) {
set_precision(x, precision(x) + (x.second - y.second));
}
x.first += y.first;
regularize(x);
return x;
};
static const auto multiplies = [](bigdecimal& x, const bigdecimal& y) -> bigdecimal& {
x.first *= y.first;
x.second += y.second;
regularize(x);
return x;
};
static const auto compare_3way = [](const bigdecimal& x, const bigdecimal& y) {
if (!x.first.m_positive && y.first.m_positive) return -1;
if (x.first.m_positive && !y.first.m_positive) return 1;
return [&]() {
if (x.second <= y.second) {
if (const auto comp = ::tools::bigint::compare_3way(precision(x), precision(y) + (y.second - x.second)); comp != 0) {
return comp;
}
for (::std::size_t i = 0; i < precision(x); ++i) {
if (const auto comp = ::tools::bigint::compare_3way(x.first.m_digits[precision(x) - 1 - i], precision(y) >= i + 1 ? y.first.m_digits[precision(y) - 1 - i] : 0); comp != 0) {
return comp;
}
}
} else {
if (const auto comp = ::tools::bigint::compare_3way(precision(x) + (x.second - y.second), precision(y)); comp != 0) {
return comp;
}
for (::std::size_t i = 0; i < precision(y); ++i) {
if (const auto comp = ::tools::bigint::compare_3way(precision(x) >= i + 1 ? x.first.m_digits[precision(x) - 1 - i] : 0, y.first.m_digits[precision(y) - 1 - i]); comp != 0) {
return comp;
}
}
}
return 0;
}() * (x.first.m_positive ? 1 : -1);
};
const bool r_positive = this->m_positive == other.m_positive;
if (!this->m_positive) {
this->negate();
}
const ::std::size_t inv_final_goal_precision = this->m_digits.size() - other.m_digits.size() + 2;
const ::std::size_t inv_first_goal_precision = ::std::min<::std::size_t>(inv_final_goal_precision, 3);
bigdecimal o(other, 0);
make_abs(o);
set_precision(o, ::std::min<::std::size_t>(other.m_digits.size(), 6));
bigdecimal prev_inv(::tools::bigint(0), 0);
bigdecimal inv(::tools::bigint(1), -::tools::ssize(other.m_digits));
while (compare_3way(prev_inv, inv) != 0) {
prev_inv = inv;
negate(inv);
multiplies(inv, o);
bigdecimal two(::tools::bigint(2), 0);
plus(inv, two);
multiplies(inv, prev_inv);
set_precision(inv, ::std::min(precision(inv), inv_first_goal_precision));
}
if (inv_first_goal_precision < inv_final_goal_precision) {
prev_inv = bigdecimal(::tools::bigint(0), 0);
while (compare_3way(prev_inv, inv) != 0) {
prev_inv = inv;
negate(inv);
multiplies(inv, o);
bigdecimal two(::tools::bigint(2), 0);
plus(inv, two);
multiplies(inv, prev_inv);
set_precision(inv, ::std::min(precision(prev_inv) * 2, inv_final_goal_precision));
const ::std::size_t o_precision = precision(o);
o = bigdecimal(other, 0);
make_abs(o);
set_precision(o, ::std::min(o_precision * 2, other.m_digits.size()));
}
}
set_precision(inv, inv_final_goal_precision);
o = bigdecimal(other, 0);
make_abs(o);
bigdecimal r(*this, 0);
multiplies(r, inv);
set_precision(r, precision(r) + r.second);
::tools::bigint r_plus_1 = r.first + ::tools::bigint(1);
if (*this >= r_plus_1 * o.first) {
*this = ::std::move(r_plus_1);
} else {
*this = ::std::move(r.first);
}
this->m_positive = r_positive;
return *this;
}
friend ::tools::bigint operator/(const ::tools::bigint& lhs, const ::tools::bigint& rhs) {
return ::tools::bigint(lhs) /= rhs;
}
::tools::bigint& operator%=(const ::tools::bigint& other) {
using u64 = ::std::uint_fast64_t;
static const ::tools::bigint u64_threshold((::std::numeric_limits<u64>::max() - (BASE - 1)) / BASE);
using u128 = unsigned __int128;
static const ::tools::bigint u128_threshold("34028236692093846346337460743176820");
#define TOOLS_BIGINT_NAIVE(type) do {\
if (::tools::bigint::compare_3way_abs(other, type ## _threshold) <= 0) { \
type mod = 0;\
for (::std::size_t i = other.m_digits.size(); i --> 0;) {\
mod *= BASE;\
mod += other.m_digits[i];\
}\
\
type result = 0;\
for (::std::size_t i = this->m_digits.size(); i --> 0;) {\
result *= BASE;\
result += this->m_digits[i];\
result %= mod;\
}\
\
this->m_digits.clear();\
while (result > 0) {\
this->m_digits.push_back(result % BASE);\
result /= BASE;\
}\
\
return this->regularize(0);\
}\
} while (false)
TOOLS_BIGINT_NAIVE(u64);
TOOLS_BIGINT_NAIVE(u128);
#undef TOOLS_BIGINT_NAIVE
const ::tools::bigint self = *this;
*this /= other;
this->negate();
*this *= other;
*this += self;
return *this;
}
friend ::tools::bigint operator%(const ::tools::bigint& lhs, const ::tools::bigint& rhs) {
return ::tools::bigint(lhs) %= rhs;
}
template <typename T, ::std::enable_if_t<::std::is_integral_v<T>, ::std::nullptr_t> = nullptr>
explicit operator T() const {
assert(::tools::bigint(::std::numeric_limits<T>::min()) <= *this && *this <= ::tools::bigint(::std::numeric_limits<T>::max()));
T result = 0;
for (::std::size_t i = this->m_digits.size(); i --> 0;) {
result = result * BASE + this->m_digits[i] * (this->m_positive ? 1 : -1);
}
return result;
}
explicit operator double() const {
long double result = 0.0;
const ::std::size_t precision = this->size();
for (::std::size_t i = 0; i < ::std::numeric_limits<long double>::digits10; ++i) {
result = result * 10.0L + (precision >= i + 1 ? (*this)[precision - 1 - i] : 0) * this->signum();
}
result *= ::std::pow(10.0L, static_cast<long double>(precision) - static_cast<long double>(::std::numeric_limits<long double>::digits10));
return static_cast<double>(result);
}
friend ::std::istream& operator>>(::std::istream& is, ::tools::bigint& self) {
::std::string s;
is >> s;
self = ::tools::bigint(s);
return is;
}
friend ::std::ostream& operator<<(::std::ostream& os, const ::tools::bigint& self) {
if (!self.m_positive) {
os << '-';
}
if (self.m_digits.empty()) {
return os << '0';
}
os << self.m_digits.back();
for (::std::size_t i = 1; i < self.m_digits.size(); ++i) {
os << ::std::setw(LOG10_BASE) << ::std::setfill('0') << self.m_digits[self.m_digits.size() - 1 - i];
}
return os;
}
friend ::tools::bigint abs(::tools::bigint x);
};
inline ::tools::bigint abs(::tools::bigint x) {
if (!x.m_positive) x.negate();
return x;
}
inline ::tools::bigint gcd(::tools::bigint x, ::tools::bigint y) {
if (x.signum() < 0) x.negate();
if (y.signum() < 0) y.negate();
while (y.signum() != 0) {
x %= y;
::std::swap(x, y);
}
return x;
}
}
#line 3 "main.cpp"
int main() {
std::cin.tie(nullptr);
std::ios_base::sync_with_stdio(false);
tools::bigint A, B;
std::cin >> A >> B;
std::cout << A + B << '\n';
return 0;
}