結果
| 問題 | No.2120 場合の数の下８桁 |
| ユーザー |
 anqooqie
|
| 提出日時 | 2022-11-05 14:15:01 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 153 ms / 2,000 ms |
| コード長 | 32,586 bytes |
| コンパイル時間 | 2,915 ms |
| コンパイル使用メモリ | 235,076 KB |
| 実行使用メモリ | 9,344 KB |
| 最終ジャッジ日時 | 2024-07-19 07:41:51 |
| 合計ジャッジ時間 | 7,062 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge2 |
（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 | 152 ms
9,344 KB |
| testcase_01 | AC | 153 ms
9,344 KB |
| testcase_02 | AC | 152 ms
9,344 KB |
| testcase_03 | AC | 152 ms
9,216 KB |
| testcase_04 | AC | 151 ms
9,344 KB |
| testcase_05 | AC | 152 ms
9,216 KB |
| testcase_06 | AC | 152 ms
9,344 KB |
| testcase_07 | AC | 152 ms
9,216 KB |
| testcase_08 | AC | 152 ms
9,344 KB |
| testcase_09 | AC | 152 ms
9,344 KB |
| testcase_10 | AC | 152 ms
9,216 KB |
| testcase_11 | AC | 152 ms
9,344 KB |
| testcase_12 | AC | 153 ms
9,216 KB |
| testcase_13 | AC | 151 ms
9,216 KB |
| testcase_14 | AC | 152 ms
9,344 KB |
| testcase_15 | AC | 151 ms
9,344 KB |
| testcase_16 | AC | 152 ms
9,216 KB |
| testcase_17 | AC | 151 ms
9,216 KB |
| testcase_18 | AC | 152 ms
9,216 KB |
| testcase_19 | AC | 152 ms
9,344 KB |
ソースコード
#line 1 "main.cpp"
#include <bits/stdc++.h>
#line 1 "/home/anqooqie/.proconlib/lib/ac-library/atcoder/modint.hpp"
#line 6 "/home/anqooqie/.proconlib/lib/ac-library/atcoder/modint.hpp"
#include <type_traits>
#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/tools/extended_lucas.hpp"
#line 1 "/home/anqooqie/.proconlib/tools/prime_factorization.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 1 "/home/anqooqie/.proconlib/tools/mod.hpp"
#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 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 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 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/floor_log2.hpp"
#line 1 "/home/anqooqie/.proconlib/tools/popcount.hpp"
#line 8 "/home/anqooqie/.proconlib/tools/popcount.hpp"
namespace tools {
template <typename T>
T popcount(T x) {
static_assert(::std::is_integral_v<T>);
assert(x >= 0);
if constexpr (::std::is_signed_v<T>) {
return static_cast<T>(::tools::popcount<::std::make_unsigned_t<T>>(x));
} else {
const auto log2 = [](const int w) {
if (w == 8) return 3;
if (w == 16) return 4;
if (w == 32) return 5;
if (w == 64) return 6;
return -1;
};
static_assert(log2(::std::numeric_limits<T>::digits) >= 0);
if constexpr (::std::numeric_limits<T>::digits == 8) {
x = (x & UINT8_C(0x55)) + (x >> 1 & UINT8_C(0x55));
x = (x & UINT8_C(0x33)) + (x >> 2 & UINT8_C(0x33));
x = (x & UINT8_C(0x0f)) + (x >> 4 & UINT8_C(0x0f));
} else if constexpr (::std::numeric_limits<T>::digits == 16) {
x = (x & UINT16_C(0x5555)) + (x >> 1 & UINT16_C(0x5555));
x = (x & UINT16_C(0x3333)) + (x >> 2 & UINT16_C(0x3333));
x = (x & UINT16_C(0x0f0f)) + (x >> 4 & UINT16_C(0x0f0f));
x = (x & UINT16_C(0x00ff)) + (x >> 8 & UINT16_C(0x00ff));
} else if constexpr (::std::numeric_limits<T>::digits == 32) {
x = (x & UINT32_C(0x55555555)) + (x >> 1 & UINT32_C(0x55555555));
x = (x & UINT32_C(0x33333333)) + (x >> 2 & UINT32_C(0x33333333));
x = (x & UINT32_C(0x0f0f0f0f)) + (x >> 4 & UINT32_C(0x0f0f0f0f));
x = (x & UINT32_C(0x00ff00ff)) + (x >> 8 & UINT32_C(0x00ff00ff));
x = (x & UINT32_C(0x0000ffff)) + (x >> 16 & UINT32_C(0x0000ffff));
} else if constexpr (::std::numeric_limits<T>::digits == 64) {
x = (x & UINT64_C(0x5555555555555555)) + (x >> 1 & UINT64_C(0x5555555555555555));
x = (x & UINT64_C(0x3333333333333333)) + (x >> 2 & UINT64_C(0x3333333333333333));
x = (x & UINT64_C(0x0f0f0f0f0f0f0f0f)) + (x >> 4 & UINT64_C(0x0f0f0f0f0f0f0f0f));
x = (x & UINT64_C(0x00ff00ff00ff00ff)) + (x >> 8 & UINT64_C(0x00ff00ff00ff00ff));
x = (x & UINT64_C(0x0000ffff0000ffff)) + (x >> 16 & UINT64_C(0x0000ffff0000ffff));
x = (x & UINT64_C(0x00000000ffffffff)) + (x >> 32 & UINT64_C(0x00000000ffffffff));
}
return x;
}
}
}
#line 8 "/home/anqooqie/.proconlib/tools/floor_log2.hpp"
namespace tools {
template <typename T>
T floor_log2(T x) {
static_assert(::std::is_integral_v<T>);
assert(x > 0);
if constexpr (::std::is_signed_v<T>) {
return static_cast<T>(::tools::floor_log2<::std::make_unsigned_t<T>>(x));
} else {
const auto log2 = [](const int w) {
if (w == 8) return 3;
if (w == 16) return 4;
if (w == 32) return 5;
if (w == 64) return 6;
return -1;
};
static_assert(log2(::std::numeric_limits<T>::digits) >= 0);
x |= (x >> 1);
x |= (x >> 2);
x |= (x >> 4);
if constexpr (::std::numeric_limits<T>::digits > 8) x |= (x >> 8);
if constexpr (::std::numeric_limits<T>::digits > 16) x |= (x >> 16);
if constexpr (::std::numeric_limits<T>::digits > 32) x |= (x >> 32);
return ::tools::popcount(x) - static_cast<T>(1);
}
}
}
#line 15 "/home/anqooqie/.proconlib/tools/prime_factorization.hpp"
namespace tools {
template <typename T>
::std::vector<T> prime_factorization(T n) {
assert(1 <= n && n <= 1000000000000000000);
::std::vector<T> result;
if (n == 1) return result;
::std::queue<::std::pair<T, T>> factors({::std::pair<T, T>(n, 1)});
while (!factors.empty()) {
const T factor = factors.front().first;
const T occurrences = factors.front().second;
factors.pop();
if (::tools::is_prime(factor)) {
for (T i = 0; i < occurrences; ++i) {
result.push_back(factor);
}
} else {
const T m = ::tools::pow2((::tools::floor_log2(factor) + 1) / 8);
for (T c = 1; ; ++c) {
const auto f = [&](T& x) {
x = ::tools::prod_mod(x, x, factor);
x += c;
if (x >= factor) x -= factor;
};
T y = 2;
T r = 1;
T q = 1;
T x, g, ys;
do {
x = y;
for (T i = 0; i < r; ++i) {
f(y);
}
T k = 0;
do {
ys = y;
for (T i = 0; i < ::std::min(m, r - k); ++i) {
f(y);
q = ::tools::prod_mod(q, ::std::abs(x - y), factor);
}
g = ::std::gcd(q, factor);
k += m;
} while (k < r && g == 1);
r *= 2;
} while (g == 1);
if (g == factor) {
do {
f(ys);
g = ::std::gcd(::std::abs(x - ys), factor);
} while (g == 1);
}
if (g < factor) {
T h = factor / g;
if (h < g) ::std::swap(g, h);
T n = 1;
while (h % g == 0) {
h /= g;
++n;
}
factors.emplace(g, occurrences * n);
if (h > 1) factors.emplace(h, occurrences);
break;
}
}
}
}
::std::sort(result.begin(), result.end());
return result;
}
}
#line 1 "/home/anqooqie/.proconlib/tools/run_length.hpp"
#line 8 "/home/anqooqie/.proconlib/tools/run_length.hpp"
namespace tools {
template <typename InputIterator, typename OutputIterator>
void run_length(const InputIterator& begin, const InputIterator& end, OutputIterator result) {
using T = typename ::std::iterator_traits<InputIterator>::value_type;
if (begin == end) return;
::std::pair<T, ::std::size_t> prev;
for (auto [it, breaks] = ::std::make_pair(begin, false); !breaks; breaks = it == end, it = ::std::next(it, breaks ? 0 : 1)) {
bool flg1, flg2;
if (it == begin) {
flg1 = false;
flg2 = true;
} else if (it == end) {
flg1 = true;
flg2 = false;
} else if (*it != prev.first) {
flg1 = true;
flg2 = true;
} else {
flg1 = false;
flg2 = false;
}
if (flg1 || flg2) {
if (flg1) {
*result = prev;
++result;
}
if (flg2) {
prev.first = *it;
prev.second = 1;
}
} else {
++prev.second;
}
}
}
}
#line 1 "/home/anqooqie/.proconlib/tools/garner.hpp"
#line 1 "/home/anqooqie/.proconlib/tools/inv_mod.hpp"
#line 1 "/home/anqooqie/.proconlib/tools/extgcd.hpp"
#line 7 "/home/anqooqie/.proconlib/tools/extgcd.hpp"
namespace tools {
template <typename T>
::std::tuple<T, T, T> extgcd(T prev_r, T r) {
T prev_s(1);
T prev_t(0);
T s(0);
T t(1);
while (r != 0) {
const T q = ::tools::quo(prev_r, r);
::std::tie(prev_r, r) = ::std::make_pair(r, prev_r - q * r);
::std::tie(prev_s, s) = ::std::make_pair(s, prev_s - q * s);
::std::tie(prev_t, t) = ::std::make_pair(t, prev_t - q * t);
}
if (prev_r < T(0)) prev_r = -prev_r;
return ::std::make_tuple(prev_s, prev_t, prev_r);
}
}
#line 7 "/home/anqooqie/.proconlib/tools/inv_mod.hpp"
namespace tools {
template <typename T1, typename T2>
constexpr T2 inv_mod(const T1 x, const T2 m) {
const auto [x0, y0, gcd] = ::tools::extgcd(x, m);
assert(gcd == 1);
return ::tools::mod(x0, m);
}
}
#line 9 "/home/anqooqie/.proconlib/tools/garner.hpp"
// Source: https://qiita.com/drken/items/ae02240cd1f8edfc86fd
// License: unknown
// Author: drken
namespace tools {
template <typename Iterator, typename ModType>
::std::pair<long long, long long> garner(const Iterator& begin, const Iterator& end, const ModType& mod) {
::std::vector<long long> b, m;
for (auto it = begin; it != end; ++it) {
b.push_back(::tools::mod(it->first, it->second));
m.push_back(it->second);
}
auto lcm = 1LL;
for (::std::size_t i = 0; i < b.size(); ++i) {
(lcm *= m[i]) %= mod;
}
m.push_back(mod);
::std::vector<long long> coeffs(m.size(), 1);
::std::vector<long long> constants(m.size(), 0);
for (::std::size_t k = 0; k < b.size(); ++k) {
long long t = ::tools::mod((b[k] - constants[k]) * ::tools::inv_mod(coeffs[k], m[k]), m[k]);
for (::std::size_t i = k + 1; i < m.size(); ++i) {
(constants[i] += t * coeffs[i]) %= m[i];
(coeffs[i] *= m[k]) %= m[i];
}
}
return ::std::make_pair(constants.back(), lcm);
}
template <typename M, typename Iterator>
::std::pair<M, M> garner(const Iterator& begin, const Iterator& end) {
const auto [y, z] = ::tools::garner(begin, end, M::mod());
return ::std::make_pair(M::raw(y), M::raw(z));
}
}
#line 11 "/home/anqooqie/.proconlib/tools/extended_lucas.hpp"
namespace tools {
// Source: https://w.atwiki.jp/uwicoder/pages/2118.html#id_6779f709
// License: unknown
// Author: uwi
template <class M>
class extended_lucas {
private:
class prime_power {
private:
::std::vector<long long> fact;
::std::vector<long long> ifact;
public:
long long p;
long long q;
long long P;
prime_power(const long long p, const long long q) : p(p), q(q) {
this->P = 1;
for (long long i = 0; i < q; ++i) {
this->P *= p;
}
this->fact.resize(this->P + 1);
this->ifact.resize(this->P + 1);
this->fact[0] = 1 % this->P;
for (long long i = 1; i <= this->P; ++i) {
this->fact[i] = this->fact[i - 1] * (i % p == 0 ? 1 : i) % this->P;
}
for (long long i = 0; i <= this->P; ++i) {
long long ret = 1 % this->P;
long long mul = this->fact[i];
for (long long n = this->P / p * (p - 1) - 1; n > 0; n /= 2) {
if ((n & 1) == 1) {
ret = (ret * mul) % P;
}
mul = (mul * mul) % P;
}
this->ifact[i] = ret;
}
}
long long combination(long long n, long long r) const {
assert(0 <= r && r <= n);
long long z = n - r;
long long e0 = 0;
for (long long u = n / this->p; u > 0; u /= this->p) e0 += u;
for (long long u = r / this->p; u > 0; u /= this->p) e0 -= u;
for (long long u = z / this->p; u > 0; u /= this->p) e0 -= u;
long long em = 0;
for (long long u = n / this->P; u > 0; u /= this->p) em += u;
for (long long u = r / this->P; u > 0; u /= this->p) em -= u;
for (long long u = z / this->P; u > 0; u /= this->p) em -= u;
long long ret = 1 % this->P;
while (n > 0) {
ret = ret * this->fact[n % this->P] % this->P * this->ifact[r % this->P] % this->P * this->ifact[z % this->P] % this->P;
n /= this->p;
r /= this->p;
z /= this->p;
}
for (long long i = 0; i < e0; ++i) {
ret = ret * this->p % this->P;
}
if (!(this->p == 2 && this->q >= 3) && (em & 1) == 1) {
ret = (this->P - ret) % this->P;
}
return ret;
}
};
::std::vector<::tools::extended_lucas<M>::prime_power> prime_powers;
public:
extended_lucas() {
const auto prime_factors = ::tools::prime_factorization(M::mod());
::std::vector<::std::pair<long long, long long>> distinct_prime_factors;
::tools::run_length(prime_factors.begin(), prime_factors.end(), ::std::back_inserter(distinct_prime_factors));
for (const auto& [p, q] : distinct_prime_factors) {
this->prime_powers.emplace_back(p, q);
}
}
extended_lucas(const ::tools::extended_lucas<M>&) = default;
extended_lucas(::tools::extended_lucas<M>&&) = default;
~extended_lucas() = default;
::tools::extended_lucas<M>& operator=(const ::tools::extended_lucas<M>&) = default;
::tools::extended_lucas<M>& operator=(::tools::extended_lucas<M>&&) = default;
M combination(const long long n, const long long r) const {
if (n < 0 || r < 0 || r > n) return M::raw(0);
::std::vector<std::pair<long long, long long>> answers;
answers.reserve(this->prime_powers.size());
for (const auto& prime_power : this->prime_powers) {
answers.emplace_back(prime_power.combination(n, r), prime_power.P);
}
return ::tools::garner<M>(answers.begin(), answers.end()).first;
}
};
}
#line 4 "main.cpp"
using ll = long long;
using mint = atcoder::static_modint<100000000>;
tools::extended_lucas<mint> cache;
int main() {
std::cin.tie(nullptr);
std::ios_base::sync_with_stdio(false);
ll M, N;
std::cin >> M >> N;
std::cout << std::setw(8) << std::setfill('0') << cache.combination(M, N).val() << '\n';
return 0;
}