#945232 (C++11) No.2613 Sum of Combination

• 問題: No.2613 Sum of Combination
• ユーザー: leaf_1415
• 提出日時: 2024-01-19 23:09:56
• 言語: C++11 (gcc 11.4.0)
• 結果: AC
• 実行時間: 628 ms / 4,500 ms
• コード長: 11,582 bytes
• コンパイル時間: 1,629 ms
• コンパイル使用メモリ: 122,424 KB
• 実行使用メモリ: 23,864 KB
• 最終ジャッジ日時: 2024-01-19 23:10:15
• 合計ジャッジ時間: 17,957 ms
• ジャッジサーバーID （参考情報）: judge12 / judge14

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	10 ms; 8,344 KB
testcase_01	AC	10 ms; 8,344 KB
testcase_02	AC	21 ms; 8,848 KB
testcase_03	AC	10 ms; 8,344 KB
testcase_04	AC	10 ms; 8,344 KB
testcase_05	AC	10 ms; 8,344 KB
testcase_06	AC	10 ms; 8,344 KB
testcase_07	AC	10 ms; 8,348 KB
testcase_08	AC	11 ms; 8,360 KB
testcase_09	AC	10 ms; 8,348 KB
testcase_10	AC	10 ms; 8,348 KB
testcase_11	AC	10 ms; 8,352 KB
testcase_12	AC	12 ms; 8,352 KB
testcase_13	AC	27 ms; 8,808 KB
testcase_14	AC	26 ms; 8,820 KB
testcase_15	AC	19 ms; 8,532 KB
testcase_16	AC	26 ms; 8,800 KB
testcase_17	AC	27 ms; 8,828 KB
testcase_18	AC	26 ms; 8,796 KB
testcase_19	AC	27 ms; 8,848 KB
testcase_20	AC	11 ms; 8,352 KB
testcase_21	AC	10 ms; 8,348 KB
testcase_22	AC	45 ms; 9,248 KB
testcase_23	AC	591 ms; 22,680 KB
testcase_24	AC	589 ms; 22,644 KB
testcase_25	AC	600 ms; 21,412 KB
testcase_26	AC	593 ms; 23,768 KB
testcase_27	AC	289 ms; 16,392 KB
testcase_28	AC	581 ms; 23,668 KB
testcase_29	AC	605 ms; 23,180 KB
testcase_30	AC	594 ms; 23,780 KB
testcase_31	AC	586 ms; 23,092 KB
testcase_32	AC	583 ms; 22,908 KB
testcase_33	AC	588 ms; 23,864 KB
testcase_34	AC	609 ms; 23,864 KB
testcase_35	AC	586 ms; 23,864 KB
testcase_36	AC	600 ms; 23,864 KB
testcase_37	AC	590 ms; 23,864 KB
testcase_38	AC	612 ms; 23,588 KB
testcase_39	AC	588 ms; 23,644 KB
testcase_40	AC	601 ms; 23,628 KB
testcase_41	AC	581 ms; 23,728 KB
testcase_42	AC	628 ms; 23,708 KB
testcase_43	AC	580 ms; 23,864 KB
testcase_44	AC	598 ms; 23,864 KB
testcase_45	AC	10 ms; 8,348 KB
testcase_46	AC	10 ms; 8,348 KB
testcase_47	AC	10 ms; 8,348 KB
testcase_48	AC	10 ms; 8,348 KB
testcase_49	AC	10 ms; 8,348 KB
testcase_50	AC	575 ms; 23,864 KB
testcase_51	AC	572 ms; 23,864 KB

コンパイルメッセージ

main.cpp: In function ‘int main()’:
main.cpp:279:44: warning: ‘r’ may be used uninitialized in this function [-Wmaybe-uninitialized]
  279 |         rep(i, 1, p-2) beki[i] = beki[i-1] * r % p, lg[beki[i]] = i;
      |                                  ~~~~~~~~~~^~~

ソースコード

#include <iostream>
#include <iomanip>
#include <cstdio>
#include <cmath>
#include <ctime>
#include <cstdlib>
#include <cassert>
#include <vector>
#include <list>
#include <stack>
#include <queue>
#include <deque>
#include <map>
#include <set>
#include <bitset>
#include <string>
#include <algorithm>
#include <utility>
#include <complex>
#include <array>
#include <unordered_set>
#include <unordered_map>
#define rep(x, s, t) for(ll x = (s); (x) <= (t); (x)++)
#define per(x, s, t) for(ll x = (s); (x) >= (t); (x)--)
#define reps(x, s) for(ll x = 0; (x) < (ll)(s).size(); (x)++)
#define pers(x, s) for(ll x = (ll)(s).size()-1; (x) >= 0; (x)--)
#define chmin(x, y) (x) = min((x), (y))
#define chmax(x, y) (x) = max((x), (y))
#define sz(x) ((ll)(x).size())
#define all(x) (x).begin(),(x).end()
#define rall(x) (x).rbegin(),(x).rend()
#define outl(...) dump_func(__VA_ARGS__)
#define outf(x) cout << fixed << setprecision(16) << (x) << endl
#define pb push_back
#define fi first
#define se second
#define inf 2e18
#define eps 1e-9
const double PI = 3.1415926535897932384626433;

using namespace std;

typedef long long ll;
typedef unsigned long long ull;
typedef pair<ll, ll> P;

struct edge{
	ll to, cost;
	edge(){}
	edge(ll a, ll b){ to = a, cost = b;}
};
const int dx[] = {1, 0, -1, 0}, dy[] = {0, -1, 0, 1};
const int dx8[] = {1, 1, 0, -1, -1, -1, 0, 1}, dy8[] = {0, -1, -1, -1, 0, 1, 1, 1};

const int mod = 998244353;
//const int mod = 1000000007;

struct mint{
	int x;
	mint(ll y = 0){if(y < 0 || y >= mod) y = (y%mod+mod)%mod; x = y;}
	mint(const mint &ope) {x = ope.x;}
	mint operator-(){return mint(-x);}
	mint operator+(const mint &ope){return mint(x) += ope;}
	mint operator-(const mint &ope){return mint(x) -= ope;}
	mint operator*(const mint &ope){return mint(x) *= ope;}
	mint operator/(const mint &ope){return mint(x) /= ope;}
	mint& operator+=(const mint &ope){x += ope.x; if(x >= mod) x -= mod; return *this;}
	mint& operator-=(const mint &ope){x += mod - ope.x; if(x >= mod) x -= mod; return *this;}
	mint& operator*=(const mint &ope){ll tmp = x; tmp *= ope.x, tmp %= mod; x = tmp; return *this;}
	mint& operator/=(const mint &ope){
		ll n = mod-2; mint mul = ope;
		while(n){if(n & 1) *this *= mul; mul *= mul; n >>= 1;}
		return *this;
	}
	mint inverse(){return mint(1) / *this;}
	bool operator ==(const mint &ope){return x == ope.x;}
	bool operator !=(const mint &ope){return x != ope.x;}
	bool operator <(const mint &ope)const{return x < ope.x;}
};
mint modpow(mint a, ll n){
	if(n == 0) return mint(1);
	if(n % 2) return a * modpow(a, n-1);
	else return modpow(a*a, n/2);
}
istream& operator >>(istream &is, mint &ope){ll t; is >> t, ope = mint(t); return is;}
ostream& operator <<(ostream &os, mint &ope){return os << ope.x;}
ostream& operator <<(ostream &os, const mint &ope){return os << ope.x;}

ll modpow(ll a, ll n, ll mod){
	if(n == 0) return 1;
	if(n % 2) return ((a%mod) * (modpow(a, n-1, mod)%mod)) % mod;
	else return modpow((a*a)%mod, n/2, mod) % mod;
}

vector<mint> fact, fact_inv;
void make_fact(int n){
	fact.resize(n+1), fact_inv.resize(n+1);
	fact[0] = mint(1); rep(i, 1, n) fact[i] = fact[i-1] * mint(i);
	fact_inv[n] = fact[n].inverse(); per(i, n-1, 0) fact_inv[i] = fact_inv[i+1] * mint(i+1);
}
mint comb(int n, int k){ if(n < 0 || k < 0 || n < k) return mint(0); return fact[n] * fact_inv[k] * fact_inv[n-k];}
mint perm(int n, int k){ return comb(n, k) * fact[k]; }
mint divide(int n, int k){ if(n == 0 && k == 0) return 1; return comb(n+k-1, k-1); }
template<typename T> T comb2(ll n, ll k){ if(n < 0 || k < 0 || n < k) return T(0); T ret = 1; rep(i, 1, k) ret *= n-k+i, ret /= i; return ret;}

vector<ll> prime, pvec, qrime;
void make_prime(int n){
	prime.resize(n+1);
	rep(i, 2, n){
		if(prime[i] == 0) pvec.push_back(i), prime[i] = i;
		for(auto p : pvec){ if(i*p > n || p > prime[i]) break; prime[i*p] = p;}
	}
}
void make_qrime(int n){
	qrime.resize(n+1);
	rep(i, 2, n){int ni = i / prime[i]; if(prime[i] == prime[ni]) qrime[i] = qrime[ni] * prime[i]; else qrime[i] = prime[i];}
}
void factorize(ll n, map<ll, ll> &mp){
	mp.clear();
	for(auto p : pvec) while(n % p == 0) mp[p]++, n /= p;
	if(n > 1) mp[n]++;
}

bool exceed(ll x, ll y, ll m){return y > 0 && x >= m / y + 1;}
void mark(){ cout << "*" << endl; }
void yes(){ cout << "Yes" << endl; }
void no(){ cout << "No" << endl; }
ll floor(ll a, ll b){ if(b < 0) a *= -1, b *= -1; if(a >= 0) return a/b; else return -((-a+b-1)/b); }
ll ceil(ll a, ll b){ if(b < 0) a *= -1, b *= -1; if(a >= 0) return (a+b-1)/b; else return -((-a)/b); }
ll modulo(ll a, ll b){ b = abs(b); return a - floor(a, b) * b;}
ll sgn(ll x){ if(x > 0) return 1; if(x < 0) return -1; return 0;}
ll gcd(ll a, ll b){if(b == 0) return a; return gcd(b, a%b);}
ll lcm(ll a, ll b){return a/gcd(a, b)*b;}
template<typename T> T arith(T x){return x*(x+1)/2;}
template<typename T> T arith2(T x){return x*(x+1)*(x*2+1)/6;}
ll digitnum(ll x, ll b = 10){ll ret = 0; for(; x; x /= b) ret++; return ret;}
ll digitsum(ll x, ll b = 10){ll ret = 0; for(; x; x /= b) ret += x % b; return ret;}
string lltos(ll x, ll b = 10){if(x == 0) return "0"; string ret; for(;x;x/=b) ret += x % b + '0'; reverse(all(ret)); return ret;}
ll stoll(string &s, ll b = 10){ll ret = 0; for(auto c : s) ret *= b, ret += c - '0'; return ret;}
template<typename T> void uniq(T &vec){sort(all(vec)); vec.erase(unique(all(vec)), vec.end());}
int popcount(ull x){
	x -= ((x>>1)&0x5555555555555555ULL), x = (x & 0x3333333333333333ULL) + ((x>>2) & 0x3333333333333333ULL);
	return (((x + (x>>4)) & 0x0F0F0F0F0F0F0F0FULL) * 0x0101010101010101ULL) >> 56;
}
template<typename T> vector<pair<T, ll>> rle(vector<T> vec){
	vector<pair<T, ll>> ret;
	for(auto x : vec){if(sz(ret) == 0 || ret.back().first != x) ret.push_back(P(x, 1)); else ret.back().second++;}
	return ret;
}
vector<pair<char, ll>> rle(string s){ vector<char> vec; for(auto c : s) vec.push_back(c); return rle(vec);}

template<class S, class T> pair<S, T>& operator+=(pair<S, T> &s, const pair<S, T> &t){s.first += t.first, s.second += t.second; return s;}
template<class S, class T> pair<S, T>& operator-=(pair<S, T> &s, const pair<S, T> &t){s.first -= t.first, s.second -= t.second; return s;}
template<class S, class T> pair<S, T> operator+(const pair<S, T> &s, const pair<S, T> &t){return pair<S,T>(s.first+t.first, s.second+t.second);}
template<class S, class T> pair<S, T> operator-(const pair<S, T> &s, const pair<S, T> &t){return pair<S,T>(s.first-t.first, s.second-t.second);}
template<class T> T dot(const pair<T, T> &s, const pair<T, T> &t){return s.first*t.first + s.second*t.second;}
template<class T> T cross(const pair<T, T> &s, const pair<T, T> &t){return s.first*t.second - s.second*t.first;}
template<class T> T mdist(pair<T, T> s, pair<T, T> t){return abs(s.first-t.first) + abs(s.second-t.second);}
template<class T> T cdist(pair<T, T> s, pair<T, T> t){return max(abs(s.first-t.first), abs(s.second-t.second));}
template<class T> T edist2(pair<T, T> s, pair<T, T> t){return (s.first-t.first)*(s.first-t.first) + (s.second-t.second)*(s.second-t.second);}

template<typename T> ostream& operator << (ostream& os, vector<T>& vec){reps(i, vec) os << vec[i] << " "; return os;}
template<typename T> ostream& operator << (ostream& os, const vector<T>& vec){reps(i, vec) os << vec[i] << " "; return os;}
template<typename T> ostream& operator << (ostream& os, list<T>& ls){for(auto x : ls) os << x << " "; return os;}
template<typename T> ostream& operator << (ostream& os, const list<T>& ls){for(auto x : ls) os << x << " "; return os;}
template<typename T> ostream& operator << (ostream& os, deque<T>& deq){reps(i,  deq) os << deq[i] << " "; return os;}
template<typename T, typename U> ostream& operator << (ostream& os, pair<T, U>& ope){ os << "(" << ope.first << ", " << ope.second << ")"; return os;}
template<typename T, typename U> ostream& operator << (ostream& os, const pair<T, U>& ope){ os << "(" << ope.first << ", " << ope.second << ")"; return os;}
template<typename T, typename U> ostream& operator << (ostream& os, map<T, U>& ope){ for(auto p : ope) os << "(" << p.first << ", " << p.second << "),";return os;}
template<typename T> ostream& operator << (ostream& os, set<T>& ope){for(auto x : ope) os << x << " "; return os;}
template<typename T> ostream& operator << (ostream& os, multiset<T>& ope){for(auto x : ope) os << x << " "; return os;}
template<typename T> void outa(T a[], ll s, ll t){rep(i, s, t){ cout << a[i]; if(i < t) cout << " ";} cout << endl;}
template<typename T, size_t N> ostream& operator << (ostream& os, array<T, N>& arr){reps(i, arr) os << arr[i] << " "; return os;}
template<typename T, size_t N> ostream& operator << (ostream& os, const array<T, N>& arr){reps(i, arr) os << arr[i] << " "; return os;}
void dump_func(){cout << endl;}
template <class Head, class... Tail>
void dump_func(Head &&head, Tail &&... tail){cout << head; if(sizeof...(Tail) > 0) cout << " "; dump_func(std::move(tail)...);}
template<typename T> void bssert(bool b, T t){ if(!b) cout << t << endl, exit(0); }


struct NTT_Convolution{
	NTT_Convolution(){};
	static int rev(int x, int n){
		int ret = 0;
		for(int i = 0; i < n; i++) ret <<= 1, ret |= (x>>i) & 1;
		return ret;
	}
	static void DFT(vector<mint> &f, vector<mint> &F, int n, mint root, bool inv = false)
	{
		int N = 1<<n;
		F.resize(N);
		for(int i = 0; i < N; i++) F[rev(i, n)] = f[i];
		if(inv) root = root.inverse();

		mint a, b, x, z;
		for(int i = 0; i < n; i++){
			int l = 1<<i;
			z = modpow(root, 1<<(n-(i+1)));
			for(int j = 0; j < N; j+=l*2){
				x = 1;
				for(int k = j; k < j+l; k++){
					a = F[k], b = F[k+l] * x;
					F[k] = a + b, F[k+l] = a - b, x *= z;
				}
			}
		}
		if(inv){
			mint Ninv = mint(N).inverse();
			for(int i = 0; i < N; i++) F[i] *= Ninv;
		}
	}
	static void conv(vector<mint> f, vector<mint> g, vector<mint> &dest)
	{
		ll logf = 0, logg = 0, len = f.size() + g.size();
		for(int i = f.size(); i; i /= 2) logf++;
		for(int i = g.size(); i; i /= 2) logg++;

		ll n = max(logf, logg)+1, N = 1<<n;
		f.resize(N), g.resize(N);
		mint root = modpow(mint(3), 119 * (1<<23-n));

		vector<mint> F, G;
		DFT(f, F, n, root), DFT(g, G, n, root);
		for(int i = 0; i < N; i++) F[i] *= G[i];
		DFT(F, f, n, root, true);

		f.resize(len-1);
		dest = f;
	}
};


ll n, p;
vector<mint> dp[63][2];
ll beki[200005], lg[200005];

vector<ll> pfact, pfact_inv;
void make_pfact(int n){
	pfact.resize(n+1), pfact_inv.resize(n+1);
	pfact[0] = 1; rep(i, 1, n) pfact[i] = pfact[i-1] * i % p;
	pfact_inv[n] = modpow(pfact[n], p-2, p); per(i, n-1, 0) pfact_inv[i] = pfact_inv[i+1] * (i+1) % p;
}
ll pcomb(int n, int k){ if(n < 0 || k < 0 || n < k) return 0; return pfact[n] * pfact_inv[k] % p * pfact_inv[n-k] % p;}



int main(void)
{
	ios::sync_with_stdio(0);
	cin.tie(0);
	make_fact(400005);

	cin >> n >> p;
	make_pfact(p-1);

	vector<ll> vec;
	while(n) vec.pb(n%p), n /= p;
	ll b = sz(vec);

	ll r;
	vector<ll> dvec;
	rep(i, 1, p-1) if((p-1)%i == 0) dvec.pb(i);
	rep(i, 1, p-1){
		bool flag = true;
		for(auto d : dvec){
			if(d == p-1) continue;
			if(modpow(i, d, p) == 1){
				flag = false;
				break;
			}
		}
		if(flag){
			r = i;
			break;
		}
	}

	beki[0] = 1, lg[1] = 0;
	rep(i, 1, p-2) beki[i] = beki[i-1] * r % p, lg[beki[i]] = i;

	vector<mint> fvec = {1};
	reps(i, vec){
		vector<mint> gvec(p), hvec;
		rep(j, 0, vec[i]) gvec[lg[pcomb(vec[i], j)]] += 1;
		NTT_Convolution::conv(fvec, gvec, hvec);

		fvec.resize(p);
		rep(j, 0, p-1) fvec[j] = 0;
		reps(j, hvec) fvec[j%(p-1)] += hvec[j];
	}

	mint ans = 0;
	reps(i, fvec) ans += fvec[i] * beki[i];
	outl(ans);

	return 0;
}