結果
| 問題 |
No.2613 Sum of Combination
|
| コンテスト | |
| ユーザー |
 Misuki
|
| 提出日時 | 2024-01-23 17:41:40 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 213 ms / 4,500 ms |
| コード長 | 9,975 bytes |
| コンパイル時間 | 3,730 ms |
| コンパイル使用メモリ | 232,076 KB |
| 実行使用メモリ | 14,940 KB |
| 最終ジャッジ日時 | 2024-09-28 06:49:58 |
| 合計ジャッジ時間 | 9,231 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge5 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 49 |
ソースコード
#pragma GCC optimize("O2")
#include <algorithm>
#include <array>
#include <bit>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <compare>
#include <complex>
#include <concepts>
#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 <numbers>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <ranges>
#include <set>
#include <span>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tuple>
#include <type_traits>
#include <variant>
//#define int ll
#define INT128_MAX (__int128)(((unsigned __int128) 1 << ((sizeof(__int128) * __CHAR_BIT__) - 1)) - 1)
#define INT128_MIN (-INT128_MAX - 1)
#define clock chrono::steady_clock::now().time_since_epoch().count()
#ifdef DEBUG
#define dbg(x) cout << (#x) << " = " << x << '\n'
#else
#define dbg(x)
#endif
namespace R = std::ranges;
namespace V = std::views;
using namespace std;
using ll = long long;
using ull = unsigned long long;
using ldb = long double;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
//#define double ldb
template<class T>
ostream& operator<<(ostream& os, const pair<T, T> pr) {
return os << pr.first << ' ' << pr.second;
}
template<class T, size_t N>
ostream& operator<<(ostream& os, const array<T, N> &arr) {
for(const T &X : arr)
os << X << ' ';
return os;
}
template<class T>
ostream& operator<<(ostream& os, const vector<T> &vec) {
for(const T &X : vec)
os << X << ' ';
return os;
}
template<class T>
ostream& operator<<(ostream& os, const set<T> &s) {
for(const T &x : s)
os << x << ' ';
return os;
}
/**
* template name: MontgomeryModInt
* author: Misuki
* reference: https://github.com/NyaanNyaan/library/blob/master/modint/montgomery-modint.hpp#L10
* last update: 2023/11/30
* note: mod should be a prime less than 2^30.
*/
template<uint32_t mod>
struct MontgomeryModInt {
using mint = MontgomeryModInt;
using i32 = int32_t;
using u32 = uint32_t;
using u64 = uint64_t;
static constexpr u32 get_r() {
u32 res = 1, base = mod;
for(i32 i = 0; i < 31; i++)
res *= base, base *= base;
return -res;
}
static constexpr u32 get_mod() {
return mod;
}
static constexpr u32 n2 = -u64(mod) % mod; //2^64 % mod
static constexpr u32 r = get_r(); //-P^{-1} % 2^32
u32 a;
static u32 reduce(const u64 &b) {
return (b + u64(u32(b) * r) * mod) >> 32;
}
static u32 transform(const u64 &b) {
return reduce(u64(b) * n2);
}
MontgomeryModInt() : a(0) {}
MontgomeryModInt(const int64_t &b)
: a(transform(b % mod + mod)) {}
mint pow(u64 k) const {
mint res(1), base(*this);
while(k) {
if (k & 1)
res *= base;
base *= base, k >>= 1;
}
return res;
}
mint inverse() const { return (*this).pow(mod - 2); }
u32 get() const {
u32 res = reduce(a);
return res >= mod ? res - mod : res;
}
mint& operator+=(const mint &b) {
if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod;
return *this;
}
mint& operator-=(const mint &b) {
if (i32(a -= b.a) < 0) a += 2 * mod;
return *this;
}
mint& operator*=(const mint &b) {
a = reduce(u64(a) * b.a);
return *this;
}
mint& operator/=(const mint &b) {
a = reduce(u64(a) * b.inverse().a);
return *this;
}
mint operator-() { return mint() - mint(*this); }
bool operator==(mint b) const {
return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
}
bool operator!=(mint b) const {
return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
}
friend mint operator+(mint a, mint b) { return a += b; }
friend mint operator-(mint a, mint b) { return a -= b; }
friend mint operator*(mint a, mint b) { return a *= b; }
friend mint operator/(mint a, mint b) { return a /= b; }
friend ostream& operator<<(ostream& os, const mint& b) {
return os << b.get();
}
friend istream& operator>>(istream& is, mint& b) {
int64_t val;
is >> val;
b = mint(val);
return is;
}
};
using mint = MontgomeryModInt<998244353>;
/**
* template name: NTTmint
* reference: https://judge.yosupo.jp/submission/69896
* last update: 2024/01/07
* include: mint
* remark: MOD = 2^K * C + 1, R is a primitive root modulo MOD
* remark: a.size() <= 2^K must be satisfied
* some common modulo: 998244353 = 2^23 * 119 + 1, R = 3
* 469762049 = 2^26 * 7 + 1, R = 3
* 1224736769 = 2^24 * 73 + 1, R = 3
* verify: Library Checker - Convolution
*/
template<int32_t k = 23, int32_t c = 119, int32_t r = 3, class Mint = MontgomeryModInt<998244353>>
struct NTT {
using u32 = uint32_t;
static constexpr u32 mod = (1 << k) * c + 1;
static constexpr u32 get_mod() { return mod; }
static void ntt(vector<Mint> &a, bool inverse) {
static array<Mint, 30> w, w_inv;
if (w[0] == 0) {
Mint root = 2;
while(root.pow((mod - 1) / 2) == 1) root += 1;
for(int i = 0; i < 30; i++)
w[i] = -(root.pow((mod - 1) >> (i + 2))), w_inv[i] = 1 / w[i];
}
int n = ssize(a);
if (not inverse) {
for(int m = n; m >>= 1; ) {
Mint ww = 1;
for(int s = 0, l = 0; s < n; s += 2 * m) {
for(int i = s, j = s + m; i < s + m; i++, j++) {
Mint x = a[i], y = a[j] * ww;
a[i] = x + y, a[j] = x - y;
}
ww *= w[__builtin_ctz(++l)];
}
}
} else {
for(int m = 1; m < n; m *= 2) {
Mint ww = 1;
for(int s = 0, l = 0; s < n; s += 2 * m) {
for(int i = s, j = s + m; i < s + m; i++, j++) {
Mint x = a[i], y = a[j];
a[i] = x + y, a[j] = (x - y) * ww;
}
ww *= w_inv[__builtin_ctz(++l)];
}
}
Mint inv = 1 / Mint(n);
for(Mint &x : a) x *= inv;
}
}
static vector<Mint> conv(vector<Mint> a, vector<Mint> b) {
int sz = ssize(a) + ssize(b) - 1;
int n = bit_ceil((u32)sz);
a.resize(n, 0);
ntt(a, false);
b.resize(n, 0);
ntt(b, false);
for(int i = 0; i < n; i++)
a[i] *= b[i];
ntt(a, true);
a.resize(sz);
return a;
}
};
//source: KACTL(https://github.com/kth-competitive-programming/kactl)
ull modmul(ull a, ull b, ull M) {
ll ret = a * b - M * ull(1.L / M * a * b);
return ret + M * (ret < 0) - M * (ret >= (ll)M);
}
ull modpow(ull b, ull e, ull mod) {
ull ans = 1;
for (; e; b = modmul(b, b, mod), e /= 2)
if (e & 1) ans = modmul(ans, b, mod);
return ans;
}
bool isPrime(ull n) {
if (n < 2 || n % 6 % 4 != 1) return (n | 1) == 3;
ull A[] = {2, 325, 9375, 28178, 450775, 9780504, 1795265022},
s = __builtin_ctzll(n-1), d = n >> s;
for (ull a : A) { // ^ count trailing zeroes
ull p = modpow(a%n, d, n), i = s;
while (p != 1 && p != n - 1 && a % n && i--)
p = modmul(p, p, n);
if (p != n-1 && i != s) return 0;
}
return 1;
}
ull pollard(ull n) {
static mt19937_64 rng(clock);
uniform_int_distribution<ull> unif(0, n - 1);
ull c = 1;
auto f = [n, &c](ull x) { return modmul(x, x, n) + c % n; };
ull x = 0, y = 0, t = 30, prd = 2, i = 1, q;
while (t++ % 40 || __gcd(prd, n) == 1) {
if (x == y) c = unif(rng), x = ++i, y = f(x);
if ((q = modmul(prd, max(x,y) - min(x,y), n))) prd = q;
x = f(x), y = f(f(y));
}
return __gcd(prd, n);
}
vector<ull> factor(ull n) {
if (n == 1) return {};
if (isPrime(n)) return {n};
ull x = pollard(n);
auto l = factor(x), r = factor(n / x);
l.insert(l.end(), r.begin(), r.end());
return l;
}
//#include "fastFactorize.cpp"
ull primitiveRoot(ull p) {
auto fac = factor(p - 1);
R::sort(fac);
fac.resize(unique(fac.begin(), fac.end()) - fac.begin());
auto test = [p, fac](ull x) {
for(ull d : fac)
if (modpow(x, (p - 1) / d, p) == 1)
return false;
return true;
};
static mt19937_64 rng(clock);
uniform_int_distribution<ull> unif(1, p - 1);
ull root;
while(!test(root = unif(rng)));
return root;
}
struct mulConvolution {
const int P, root;
vector<int> powR, logR;
mulConvolution(int _P) : P(_P), root(primitiveRoot(_P)), powR(P - 1), logR(P) {
for(int i = 0, tmp = 1; i < P - 1; i++, tmp = (ll)tmp * root % P)
powR[i] = tmp, logR[tmp] = i;
}
template<class Mint>
vector<Mint> transform(vector<Mint> &f) {
assert(ssize(f) == P);
vector<Mint> g(P - 1);
for(int i = 1; i < P; i++)
g[logR[i]] = f[i];
return g;
}
template<class Mint>
vector<Mint> invTransform(vector<Mint> &f) {
assert(ssize(f) == P - 1);
vector<Mint> g(P);
for(int i = 0; i < P - 1; i++)
g[powR[i]] = f[i];
return g;
}
};
int p;
int fac[200000], facInv[200000];
int C(int a, int b) {
if (b > a or b < 0) return 0;
else return (ll)fac[a] * facInv[b] % p * facInv[a - b] % p;
}
NTT ntt;
signed main() {
ios::sync_with_stdio(false), cin.tie(NULL);
ll n; cin >> n >> p;
fac[0] = 1;
for(int i = 1; i < p; i++)
fac[i] = (ll)fac[i - 1] * i % p;
facInv[p - 1] = modpow(fac[p - 1], p - 2, p);
for(int i = p - 2; i >= 0; i--)
facInv[i] = (ll)facInv[i + 1] * (i + 1) % p;
mulConvolution mu(p);
vector<mint> f(p - 1);
f[0] = 1;
while(n) {
int nd = n % p; n /= p;
vector<mint> g(p);
for(int i = 0; i < p; i++)
g[C(nd, i)] += 1;
g = mu.transform(g);
f = ntt.conv(f, g);
for(int i = p - 1; i < 2 * p - 3; i++)
f[i - (p - 1)] += f[i];
f.resize(p - 1);
}
f = mu.invTransform(f);
mint ans = 0;
for(int i = 1; i < p; i++)
ans += f[i] * i;
cout << ans << '\n';
return 0;
}