結果
| 問題 | No.3394 Big Binom |
| コンテスト | |
| ユーザー |
 NyaanNyaan
|
| 提出日時 | 2025-12-02 23:11:14 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.89.0) |
| 結果 |
RE
|
| 実行時間 | - |
| コード長 | 30,124 bytes |
| 記録 | |
| コンパイル時間 | 3,003 ms |
| コンパイル使用メモリ | 294,292 KB |
| 実行使用メモリ | 7,852 KB |
| 最終ジャッジ日時 | 2025-12-02 23:11:22 |
| 合計ジャッジ時間 | 6,707 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge1 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | RE * 4 |
| other | RE * 21 |
ソースコード
/**
* date : 2025-12-02 23:10:31
* author : Nyaan
*/
#define NDEBUG
using namespace std;
// intrinstic
#include <immintrin.h>
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tr2/dynamic_bitset>
#include <tuple>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
// utility
namespace Nyaan {
using ll = long long;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;
template <typename T>
using V = vector<T>;
template <typename T>
using VV = vector<vector<T>>;
using vi = vector<int>;
using vl = vector<long long>;
using vd = V<double>;
using vs = V<string>;
using vvi = vector<vector<int>>;
using vvl = vector<vector<long long>>;
template <typename T>
using minpq = priority_queue<T, vector<T>, greater<T>>;
template <typename T, typename U>
struct P : pair<T, U> {
template <typename... Args>
constexpr P(Args... args) : pair<T, U>(args...) {}
using pair<T, U>::first;
using pair<T, U>::second;
P &operator+=(const P &r) {
first += r.first;
second += r.second;
return *this;
}
P &operator-=(const P &r) {
first -= r.first;
second -= r.second;
return *this;
}
P &operator*=(const P &r) {
first *= r.first;
second *= r.second;
return *this;
}
template <typename S>
P &operator*=(const S &r) {
first *= r, second *= r;
return *this;
}
P operator+(const P &r) const { return P(*this) += r; }
P operator-(const P &r) const { return P(*this) -= r; }
P operator*(const P &r) const { return P(*this) *= r; }
template <typename S>
P operator*(const S &r) const {
return P(*this) *= r;
}
P operator-() const { return P{-first, -second}; }
};
using pl = P<ll, ll>;
using pi = P<int, int>;
using vp = V<pl>;
constexpr int inf = 1001001001;
constexpr long long infLL = 4004004004004004004LL;
template <typename T>
int sz(const T &t) {
return t.size();
}
template <typename T, typename U>
inline bool amin(T &x, U y) {
return (y < x) ? (x = y, true) : false;
}
template <typename T, typename U>
inline bool amax(T &x, U y) {
return (x < y) ? (x = y, true) : false;
}
template <typename T>
inline T Max(const vector<T> &v) {
return *max_element(begin(v), end(v));
}
template <typename T>
inline T Min(const vector<T> &v) {
return *min_element(begin(v), end(v));
}
template <typename T>
inline long long Sum(const vector<T> &v) {
return accumulate(begin(v), end(v), 0LL);
}
template <typename T>
int lb(const vector<T> &v, const T &a) {
return lower_bound(begin(v), end(v), a) - begin(v);
}
template <typename T>
int ub(const vector<T> &v, const T &a) {
return upper_bound(begin(v), end(v), a) - begin(v);
}
constexpr long long TEN(int n) {
long long ret = 1, x = 10;
for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1);
return ret;
}
template <typename T, typename U>
pair<T, U> mkp(const T &t, const U &u) {
return make_pair(t, u);
}
template <typename T>
vector<T> mkrui(const vector<T> &v, bool rev = false) {
vector<T> ret(v.size() + 1);
if (rev) {
for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1];
} else {
for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i];
}
return ret;
};
template <typename T>
vector<T> mkuni(const vector<T> &v) {
vector<T> ret(v);
sort(ret.begin(), ret.end());
ret.erase(unique(ret.begin(), ret.end()), ret.end());
return ret;
}
template <typename F>
vector<int> mkord(int N, F f) {
vector<int> ord(N);
iota(begin(ord), end(ord), 0);
sort(begin(ord), end(ord), f);
return ord;
}
template <typename T>
vector<int> mkinv(vector<T> &v) {
int max_val = *max_element(begin(v), end(v));
vector<int> inv(max_val + 1, -1);
for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i;
return inv;
}
vector<int> mkiota(int n) {
vector<int> ret(n);
iota(begin(ret), end(ret), 0);
return ret;
}
template <typename T>
T mkrev(const T &v) {
T w{v};
reverse(begin(w), end(w));
return w;
}
template <typename T>
bool nxp(T &v) {
return next_permutation(begin(v), end(v));
}
// 返り値の型は入力の T に依存
// i 要素目 : [0, a[i])
template <typename T>
vector<vector<T>> product(const vector<T> &a) {
vector<vector<T>> ret;
vector<T> v;
auto dfs = [&](auto rc, int i) -> void {
if (i == (int)a.size()) {
ret.push_back(v);
return;
}
for (int j = 0; j < a[i]; j++) v.push_back(j), rc(rc, i + 1), v.pop_back();
};
dfs(dfs, 0);
return ret;
}
// F : function(void(T&)), mod を取る操作
// T : 整数型のときはオーバーフローに注意する
template <typename T>
T Power(T a, long long n, const T &I, const function<void(T &)> &f) {
T res = I;
for (; n; f(a = a * a), n >>= 1) {
if (n & 1) f(res = res * a);
}
return res;
}
// T : 整数型のときはオーバーフローに注意する
template <typename T>
T Power(T a, long long n, const T &I = T{1}) {
return Power(a, n, I, function<void(T &)>{[](T &) -> void {}});
}
template <typename T>
T Rev(const T &v) {
T res = v;
reverse(begin(res), end(res));
return res;
}
template <typename T>
vector<T> Transpose(const vector<T> &v) {
using U = typename T::value_type;
if(v.empty()) return {};
int H = v.size(), W = v[0].size();
vector res(W, T(H, U{}));
for (int i = 0; i < H; i++) {
for (int j = 0; j < W; j++) {
res[j][i] = v[i][j];
}
}
return res;
}
template <typename T>
vector<T> Rotate(const vector<T> &v, int clockwise = true) {
using U = typename T::value_type;
int H = v.size(), W = v[0].size();
vector res(W, T(H, U{}));
for (int i = 0; i < H; i++) {
for (int j = 0; j < W; j++) {
if (clockwise) {
res[W - 1 - j][i] = v[i][j];
} else {
res[j][H - 1 - i] = v[i][j];
}
}
}
return res;
}
} // namespace Nyaan
// bit operation
namespace Nyaan {
__attribute__((target("popcnt"))) inline int popcnt(const u64 &a) {
return __builtin_popcountll(a);
}
inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; }
template <typename T>
inline int gbit(const T &a, int i) {
return (a >> i) & 1;
}
template <typename T>
inline void sbit(T &a, int i, bool b) {
if (gbit(a, i) != b) a ^= T(1) << i;
}
constexpr long long PW(int n) { return 1LL << n; }
constexpr long long MSK(int n) { return (1LL << n) - 1; }
} // namespace Nyaan
// inout
namespace Nyaan {
template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
os << p.first << " " << p.second;
return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p) {
is >> p.first >> p.second;
return is;
}
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
int s = (int)v.size();
for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
for (auto &x : v) is >> x;
return is;
}
istream &operator>>(istream &is, __int128_t &x) {
string S;
is >> S;
x = 0;
int flag = 0;
for (auto &c : S) {
if (c == '-') {
flag = true;
continue;
}
x *= 10;
x += c - '0';
}
if (flag) x = -x;
return is;
}
istream &operator>>(istream &is, __uint128_t &x) {
string S;
is >> S;
x = 0;
for (auto &c : S) {
x *= 10;
x += c - '0';
}
return is;
}
ostream &operator<<(ostream &os, __int128_t x) {
if (x == 0) return os << 0;
if (x < 0) os << '-', x = -x;
string S;
while (x) S.push_back('0' + x % 10), x /= 10;
reverse(begin(S), end(S));
return os << S;
}
ostream &operator<<(ostream &os, __uint128_t x) {
if (x == 0) return os << 0;
string S;
while (x) S.push_back('0' + x % 10), x /= 10;
reverse(begin(S), end(S));
return os << S;
}
void in() {}
template <typename T, class... U>
void in(T &t, U &...u) {
cin >> t;
in(u...);
}
void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u) {
cout << t;
if (sizeof...(u)) cout << sep;
out(u...);
}
struct IoSetupNya {
IoSetupNya() {
cin.tie(nullptr);
ios::sync_with_stdio(false);
cout << fixed << setprecision(15);
cerr << fixed << setprecision(7);
}
} iosetupnya;
} // namespace Nyaan
// debug
#ifdef NyaanDebug
#define trc(...) (void(0))
#else
#define trc(...) (void(0))
#endif
#ifdef NyaanLocal
#define trc2(...) (void(0))
#else
#define trc2(...) (void(0))
#endif
// macro
#define each(x, v) for (auto&& x : v)
#define each2(x, y, v) for (auto&& [x, y] : v)
#define all(v) (v).begin(), (v).end()
#define rep(i, N) for (long long i = 0; i < (long long)(N); i++)
#define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--)
#define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++)
#define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--)
#define reg(i, a, b) for (long long i = (a); i < (b); i++)
#define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--)
#define fi first
#define se second
#define ini(...) \
int __VA_ARGS__; \
in(__VA_ARGS__)
#define inl(...) \
long long __VA_ARGS__; \
in(__VA_ARGS__)
#define ins(...) \
string __VA_ARGS__; \
in(__VA_ARGS__)
#define in2(s, t) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i]); \
}
#define in3(s, t, u) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i], u[i]); \
}
#define in4(s, t, u, v) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i], u[i], v[i]); \
}
#define die(...) \
do { \
Nyaan::out(__VA_ARGS__); \
return; \
} while (0)
namespace Nyaan {
void solve();
}
int main() { Nyaan::solve(); }
//
#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`
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);
} // namespace internal
} // namespace atcoder
namespace atcoder {
long long pow_mod(long long x, long long n, int m) {
assert(0 <= n && 1 <= m);
if (m == 1) return 0;
internal::barrett bt((unsigned int)(m));
unsigned int r = 1, y = (unsigned int)(internal::safe_mod(x, m));
while (n) {
if (n & 1) r = bt.mul(r, y);
y = bt.mul(y, y);
n >>= 1;
}
return r;
}
long long inv_mod(long long x, long long m) {
assert(1 <= m);
auto z = internal::inv_gcd(x, m);
assert(z.first == 1);
return z.second;
}
// (rem, mod)
std::pair<long long, long long> crt(const std::vector<long long>& r,
const std::vector<long long>& m) {
assert(r.size() == m.size());
int n = int(r.size());
// Contracts: 0 <= r0 < m0
long long r0 = 0, m0 = 1;
for (int i = 0; i < n; i++) {
assert(1 <= m[i]);
long long r1 = internal::safe_mod(r[i], m[i]), m1 = m[i];
if (m0 < m1) {
std::swap(r0, r1);
std::swap(m0, m1);
}
if (m0 % m1 == 0) {
if (r0 % m1 != r1) return {0, 0};
continue;
}
// assume: m0 > m1, lcm(m0, m1) >= 2 * max(m0, m1)
// (r0, m0), (r1, m1) -> (r2, m2 = lcm(m0, m1));
// r2 % m0 = r0
// r2 % m1 = r1
// -> (r0 + x*m0) % m1 = r1
// -> x*u0*g % (u1*g) = (r1 - r0) (u0*g = m0, u1*g = m1)
// -> x = (r1 - r0) / g * inv(u0) (mod u1)
// im = inv(u0) (mod u1) (0 <= im < u1)
long long g, im;
std::tie(g, im) = internal::inv_gcd(m0, m1);
long long u1 = (m1 / g);
// |r1 - r0| < (m0 + m1) <= lcm(m0, m1)
if ((r1 - r0) % g) return {0, 0};
// u1 * u1 <= m1 * m1 / g / g <= m0 * m1 / g = lcm(m0, m1)
long long x = (r1 - r0) / g % u1 * im % u1;
// |r0| + |m0 * x|
// < m0 + m0 * (u1 - 1)
// = m0 + m0 * m1 / g - m0
// = lcm(m0, m1)
r0 += x * m0;
m0 *= u1; // -> lcm(m0, m1)
if (r0 < 0) r0 += m0;
}
return {r0, m0};
}
long long floor_sum(long long n, long long m, long long a, long long b) {
long long ans = 0;
if (a < 0) {
unsigned long long a2 = internal::safe_mod(a, m);
ans -= 1ULL * n * (n - 1) / 2 * ((a2 - a) / m);
a = a2;
}
if (b < 0) {
unsigned long long b2 = internal::safe_mod(b, m);
ans -= 1ULL * n * ((b2 - b) / m);
b = b2;
}
if (a >= m) {
ans += (n - 1) * n * (a / m) / 2;
a %= m;
}
if (b >= m) {
ans += n * (b / m);
b %= m;
}
long long y_max = (a * n + b) / m, x_max = (y_max * m - b);
if (y_max == 0) return ans;
ans += (n - (x_max + a - 1) / a) * y_max;
ans += floor_sum(y_max, a, m, (a - x_max % a) % a);
return ans;
}
} // namespace atcoder
using namespace std;
struct Barrett {
using u32 = unsigned int;
using i64 = long long;
using u64 = unsigned long long;
u32 m;
u64 im;
Barrett() : m(), im() {}
Barrett(int n) : m(n), im(u64(-1) / m + 1) {}
constexpr inline i64 quo(u64 n) {
u64 x = u64((__uint128_t(n) * im) >> 64);
u32 r = n - x * m;
return m <= r ? x - 1 : x;
}
constexpr inline i64 rem(u64 n) {
u64 x = u64((__uint128_t(n) * im) >> 64);
u32 r = n - x * m;
return m <= r ? r + m : r;
}
constexpr inline pair<i64, int> quorem(u64 n) {
u64 x = u64((__uint128_t(n) * im) >> 64);
u32 r = n - x * m;
if (m <= r) return {x - 1, r + m};
return {x, r};
}
constexpr inline i64 pow(u64 n, i64 p) {
u32 a = rem(n), r = m == 1 ? 0 : 1;
while (p) {
if (p & 1) r = rem(u64(r) * a);
a = rem(u64(a) * a);
p >>= 1;
}
return r;
}
};
#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("avx2")
#define PRIME_POWER_BINOMIAL_M_MAX ((1LL << 30) - 1)
#define PRIME_POWER_BINOMIAL_N_MAX 20000000
struct simd_prime_binomial {
using u32 = unsigned int;
using i64 = long long;
using u64 = unsigned long long;
using m256 = __m256i;
u32 get_r(u32 _mod) {
u32 ret = _mod;
for (int i = 0; i < 4; ++i) ret *= 2 - _mod * ret;
return ret;
}
inline u32 reduce(const u64& b) {
return (b + u64(u32(b) * u32(-r)) * mod) >> 32;
}
inline u32 mul(const u32& a, const u32& b) { return reduce(u64(a) * b); }
inline u32 add(const u32& a, const u32& b) {
u32 c = a + b - 2 * mod;
if (c > 2 * mod) c += 2 * mod;
return c;
}
inline u32 cast(const i64& b) { return reduce(u64(b % mod + mod) * n2); }
inline u32 raw_cast(const u64& b) { return reduce(b * n2); }
u64 get(const u32& b) {
u32 a = reduce(b);
return a >= mod ? a - mod : a;
}
u32 inv(u32 b) {
u32 e = mod - 2, a = raw_cast(1);
while (e) {
if (e & 1) a = mul(a, b);
b = mul(b, b);
e >>= 1;
}
return a;
}
__attribute__((target("avx2"), optimize("O3", "unroll-loops"))) inline m256
simd_mulhi(const m256& a, const m256& b) {
m256 a13 = _mm256_shuffle_epi32(a, 0xF5);
m256 b13 = _mm256_shuffle_epi32(b, 0xF5);
m256 prod02 = _mm256_mul_epu32(a, b);
m256 prod13 = _mm256_mul_epu32(a13, b13);
m256 unpalo = _mm256_unpacklo_epi32(prod02, prod13);
m256 unpahi = _mm256_unpackhi_epi32(prod02, prod13);
m256 prod = _mm256_unpackhi_epi64(unpalo, unpahi);
return prod;
}
__attribute__((target("avx2"), optimize("O3", "unroll-loops"))) inline m256
simd_sub(const m256& a, const m256& b) {
m256 ret = _mm256_sub_epi32(a, b);
m256 cmp = _mm256_cmpgt_epi32(M0, ret);
m256 add = _mm256_and_si256(cmp, M2);
return _mm256_add_epi32(add, ret);
}
__attribute__((target("avx2"), optimize("O3", "unroll-loops"))) inline m256
simd_mul(const m256& A, const m256& B) {
m256 a13 = _mm256_shuffle_epi32(A, 0xF5);
m256 b13 = _mm256_shuffle_epi32(B, 0xF5);
m256 prod02 = _mm256_mul_epu32(A, B);
m256 prod13 = _mm256_mul_epu32(a13, b13);
m256 unpalo = _mm256_unpacklo_epi32(prod02, prod13);
m256 unpahi = _mm256_unpackhi_epi32(prod02, prod13);
m256 prodlo = _mm256_unpacklo_epi64(unpalo, unpahi);
m256 prodhi = _mm256_unpackhi_epi64(unpalo, unpahi);
m256 hiplm1 = _mm256_add_epi32(prodhi, M1);
m256 lomulr = _mm256_mullo_epi32(prodlo, R);
m256 lomulrmulm1 = simd_mulhi(lomulr, M1);
return _mm256_sub_epi32(hiplm1, lomulrmulm1);
}
__attribute__((target("avx2"), optimize("O3", "unroll-loops"))) inline void
transpose8_ps(__m256& row0, __m256& row1, __m256& row2, __m256& row3,
__m256& row4, __m256& row5, __m256& row6, __m256& row7) {
__m256 __t0, __t1, __t2, __t3, __t4, __t5, __t6, __t7;
__m256 __tt0, __tt1, __tt2, __tt3, __tt4, __tt5, __tt6, __tt7;
__t0 = _mm256_unpacklo_ps(row0, row1);
__t1 = _mm256_unpackhi_ps(row0, row1);
__t2 = _mm256_unpacklo_ps(row2, row3);
__t3 = _mm256_unpackhi_ps(row2, row3);
__t4 = _mm256_unpacklo_ps(row4, row5);
__t5 = _mm256_unpackhi_ps(row4, row5);
__t6 = _mm256_unpacklo_ps(row6, row7);
__t7 = _mm256_unpackhi_ps(row6, row7);
__tt0 = _mm256_shuffle_ps(__t0, __t2, _MM_SHUFFLE(1, 0, 1, 0));
__tt1 = _mm256_shuffle_ps(__t0, __t2, _MM_SHUFFLE(3, 2, 3, 2));
__tt2 = _mm256_shuffle_ps(__t1, __t3, _MM_SHUFFLE(1, 0, 1, 0));
__tt3 = _mm256_shuffle_ps(__t1, __t3, _MM_SHUFFLE(3, 2, 3, 2));
__tt4 = _mm256_shuffle_ps(__t4, __t6, _MM_SHUFFLE(1, 0, 1, 0));
__tt5 = _mm256_shuffle_ps(__t4, __t6, _MM_SHUFFLE(3, 2, 3, 2));
__tt6 = _mm256_shuffle_ps(__t5, __t7, _MM_SHUFFLE(1, 0, 1, 0));
__tt7 = _mm256_shuffle_ps(__t5, __t7, _MM_SHUFFLE(3, 2, 3, 2));
row0 = _mm256_permute2f128_ps(__tt0, __tt4, 0x20);
row1 = _mm256_permute2f128_ps(__tt1, __tt5, 0x20);
row2 = _mm256_permute2f128_ps(__tt2, __tt6, 0x20);
row3 = _mm256_permute2f128_ps(__tt3, __tt7, 0x20);
row4 = _mm256_permute2f128_ps(__tt0, __tt4, 0x31);
row5 = _mm256_permute2f128_ps(__tt1, __tt5, 0x31);
row6 = _mm256_permute2f128_ps(__tt2, __tt6, 0x31);
row7 = _mm256_permute2f128_ps(__tt3, __tt7, 0x31);
}
__attribute__((target("avx2"), optimize("O3", "unroll-loops"))) void
precalc() {
__attribute__((aligned(32))) u32 b1[32];
__attribute__((aligned(32))) __m256 b2[8];
int max = ((mod / 2) / v + 12) / 8 * 8;
f.resize(max + 1, raw_cast(1));
for (int i = 0; i < 32; i++) b1[i] = raw_cast(i + 1);
m256 A0 = _mm256_set1_epi32(b1[0]);
m256 A1 = _mm256_set1_epi32(b1[0]);
m256 A2 = _mm256_set1_epi32(b1[0]);
m256 A3 = _mm256_set1_epi32(b1[0]);
m256 B0 = _mm256_load_si256((m256*)(b1 + 0));
m256 B1 = _mm256_load_si256((m256*)(b1 + 8));
m256 B2 = _mm256_load_si256((m256*)(b1 + 16));
m256 B3 = _mm256_load_si256((m256*)(b1 + 24));
m256 DI = _mm256_set1_epi32(mod * 2 - b1[31]);
for (int i = 1; i < (int)f.size(); i += 8) {
for (int j = 0; j < 8; j++) {
for (u32 loop = 0; loop < v / 32; loop++) {
A0 = simd_mul(A0, B0), A1 = simd_mul(A1, B1);
A2 = simd_mul(A2, B2), A3 = simd_mul(A3, B3);
B0 = simd_sub(B0, DI), B1 = simd_sub(B1, DI);
B2 = simd_sub(B2, DI), B3 = simd_sub(B3, DI);
}
m256 C0 = simd_mul(A0, A1);
m256 C1 = simd_mul(A2, A3);
m256 C2 = simd_mul(C0, C1);
_mm256_store_si256((m256*)(b2 + j), C2);
}
transpose8_ps(b2[0], b2[1], b2[2], b2[3], b2[4], b2[5], b2[6], b2[7]);
m256 D0 = simd_mul(m256(b2[0]), m256(b2[1]));
m256 D1 = simd_mul(m256(b2[2]), m256(b2[3]));
m256 D2 = simd_mul(m256(b2[4]), m256(b2[5]));
m256 D3 = simd_mul(m256(b2[6]), m256(b2[7]));
m256 D4 = simd_mul(D0, D1);
m256 D5 = simd_mul(D2, D3);
m256 D6 = simd_mul(D4, D5);
_mm256_storeu_si256((m256*)(f.data() + i), D6);
}
}
u32 mod, r, n2;
Barrett bm;
m256 R, M0, M1, M2;
static constexpr u32 v = 128;
static_assert(v % 32 == 0);
vector<u32> f;
simd_prime_binomial() = default;
__attribute__((target("avx2"), optimize("O3", "unroll-loops")))
simd_prime_binomial(u32 _mod)
: mod(_mod) {
assert(2 < mod && mod < (1u << 30));
assert(mod % 2 != 0);
r = get_r(mod);
n2 = -u64(mod) % mod;
bm = Barrett(mod);
R = _mm256_set1_epi32(r);
M0 = _mm256_set1_epi32(0);
M1 = _mm256_set1_epi32(mod);
M2 = _mm256_set1_epi32(mod * 2);
precalc();
}
u32 raw_fac(u64 n) {
assert(n < mod);
if (n * 2 > mod + 2) {
u64 x = raw_fac(mod - 1 - n);
if (n % 2 == 0) x = mod * 2 - x;
return inv(x);
}
u32 a = f[n / v], i = n / v * v + 1;
u32 j = raw_cast(i), o = raw_cast(1);
while (i++ <= n) {
a = mul(a, j), j = add(j, o);
}
return a;
}
inline u32 fac(u64 n) {
if (n >= mod) return 0;
return get(raw_fac(n));
}
u32 C(long long n, long long m) {
if (n < 0 or m < 0 or n < m) return 0;
u32 num = raw_cast(1), denom = raw_cast(1);
while (n) {
long long n0, m0;
tie(n, n0) = bm.quorem(n);
tie(m, m0) = bm.quorem(m);
if (n0 < m0) return 0;
num = mul(num, raw_fac(n0));
denom = mul(denom, raw_fac(n0 - m0));
denom = mul(denom, raw_fac(m0));
}
return get(mul(num, inv(denom)));
}
};
struct prime_power_binomial {
int p, q, M;
vector<int> fac, ifac, inv;
int delta;
Barrett bm, bp;
prime_power_binomial() = default;
prime_power_binomial(int _p, int _q) : p(_p), q(_q) {
assert(1 < p && p <= PRIME_POWER_BINOMIAL_M_MAX);
assert(_q > 0);
long long m = 1;
while (_q--) {
m *= p;
assert(m <= PRIME_POWER_BINOMIAL_M_MAX);
}
M = m;
bm = Barrett(M), bp = Barrett(p);
enumerate();
delta = (p == 2 && q >= 3) ? 1 : M - 1;
}
void enumerate() {
int MX = min<int>(M, PRIME_POWER_BINOMIAL_N_MAX + 10);
fac.resize(MX);
ifac.resize(MX);
inv.resize(MX);
fac[0] = ifac[0] = inv[0] = 1;
fac[1] = ifac[1] = inv[1] = 1;
for (int i = 2; i < MX; i++) {
if (i % p == 0) {
fac[i] = fac[i - 1];
fac[i + 1] = bm.rem(1LL * fac[i - 1] * (i + 1));
i++;
} else {
fac[i] = bm.rem(1LL * fac[i - 1] * i);
}
}
ifac[MX - 1] = bm.pow(fac[MX - 1], M / p * (p - 1) - 1);
for (int i = MX - 2; i > 1; --i) {
if (i % p == 0) {
ifac[i] = bm.rem(1LL * ifac[i + 1] * (i + 1));
ifac[i - 1] = ifac[i];
i--;
} else {
ifac[i] = bm.rem(1LL * ifac[i + 1] * (i + 1));
}
}
}
long long Lucas(long long n, long long m) {
int res = 1;
while (n) {
int n0, m0;
tie(n, n0) = bp.quorem(n);
tie(m, m0) = bp.quorem(m);
if (n0 < m0) return 0;
res = bm.rem(1LL * res * fac[n0]);
int buf = bm.rem(1LL * ifac[n0 - m0] * ifac[m0]);
res = bm.rem(1LL * res * buf);
}
return res;
}
long long C(long long n, long long m) {
if (n < m || n < 0 || m < 0) return 0;
if (q == 1) return Lucas(n, m);
long long r = n - m;
int e0 = 0, eq = 0, i = 0;
int res = 1;
while (n) {
res = bm.rem(1LL * res * fac[bm.rem(n)]);
res = bm.rem(1LL * res * ifac[bm.rem(m)]);
res = bm.rem(1LL * res * ifac[bm.rem(r)]);
n = bp.quo(n);
m = bp.quo(m);
r = bp.quo(r);
int eps = n - m - r;
e0 += eps;
if (e0 >= q) return 0;
if (++i >= q) eq += eps;
}
if (eq & 1) res = bm.rem(1LL * res * delta);
res = bm.rem(1LL * res * bm.pow(p, e0));
return res;
}
};
// constraints:
// M <= 1e9 and max(N) <= 1e18
struct arbitrary_mod_binomial {
int mod;
vector<int> M1, M2;
vector<prime_power_binomial> cs1;
vector<simd_prime_binomial> cs2;
void push_cs(int i, int j, int k) {
if (i < PRIME_POWER_BINOMIAL_N_MAX || j != 1) {
cs1.emplace_back(i, j);
M1.push_back(k);
} else {
assert(j == 1);
cs2.emplace_back(i);
M2.push_back(k);
}
}
arbitrary_mod_binomial(long long md) : mod(md) {
assert(1 <= md);
assert(md <= PRIME_POWER_BINOMIAL_M_MAX);
for (int i = 2; i * i <= md; i++) {
if (md % i == 0) {
int j = 0, k = 1;
while (md % i == 0) md /= i, j++, k *= i;
push_cs(i, j, k);
}
}
if (md != 1) push_cs(md, 1, md);
assert(M1.size() == cs1.size());
assert(M2.size() == cs2.size());
}
long long C(long long n, long long m) {
if (mod == 1) return 0;
vector<long long> rem, d;
for (int i = 0; i < (int)cs1.size(); i++) {
rem.push_back(cs1[i].C(n, m));
d.push_back(M1[i]);
}
for (int i = 0; i < (int)cs2.size(); i++) {
rem.push_back(cs2[i].C(n, m));
d.push_back(M2[i]);
}
return atcoder::crt(rem, d).first;
}
};
#undef PRIME_POWER_BINOMIAL_M_MAX
#undef PRIME_POWER_BINOMIAL_N_MAX
using namespace Nyaan;
void q() {
inl(N, K);
arbitrary_mod_binomial C(998244353);
out(C.C(N, K));
}
void Nyaan::solve() {
int t = 1;
// in(t);
while (t--) q();
}