結果

問題 No.1962 Not Divide
ユーザー HIR180
提出日時 2022-06-12 12:27:53
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 1,115 ms / 2,000 ms
コード長 9,736 bytes
コンパイル時間 3,186 ms
コンパイル使用メモリ 210,116 KB
最終ジャッジ日時 2025-01-29 20:46:49
ジャッジサーバーID
（参考情報） 		judge5 / judge4
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 21
権限があれば一括ダウンロードができます
コンパイルメッセージ
main.cpp: In function ‘std::vector<long long int> BerlekampMassey(std::vector<long long int>)’:
main.cpp:345:30: warning: ‘lf’ may be used uninitialized [-Wmaybe-uninitialized]
  345 |                 vector<ll>c(i-lf-1);
      |                             ~^~~
main.cpp:333:13: note: ‘lf’ was declared here
  333 |         int lf,ld;
      |             ^~
In function ‘ll modpow(ll, ll)’,
    inlined from ‘std::vector<long long int> BerlekampMassey(std::vector<long long int>)’ at main.cpp:344:26:
main.cpp:124:32: warning: ‘ld’ may be used uninitialized [-Wmaybe-uninitialized]
  124 |                 if(n&1) res=res*x%mod;
      |                             ~~~^~
main.cpp: In function ‘std::vector<long long int> BerlekampMassey(std::vector<long long int>)’:
main.cpp:333:16: note: ‘ld’ was declared here
  333 |         int lf,ld;
      |                ^~

ソースコード

diff # 

//Let's join Kaede Takagaki Fan Club !!
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <cmath>
#include <ctime>
#include <cassert>
#include <string>
#include <algorithm>
#include <vector>
#include <queue>
#include <stack>
#include <functional>
#include <iostream>
#include <map>
#include <set>
#include <unordered_map>
#include <unordered_set>
#include <cassert>
#include <iomanip>
#include <chrono>
#include <random>
#include <bitset>
#include <complex>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
#define int long long
//#define L __int128
typedef long long ll;
typedef pair<int,int> P;
typedef pair<int,P> P1;
typedef pair<P,P> P2;
#define pu push
#define pb push_back
#define eb emplace_back
#define mp make_pair
#define eps 1e-7
#define INF 1000000000
#define a first
#define b second
#define fi first
#define sc second
//#define rng(i,a,b) for(int i=(int)(a);i<(int)(b);i++)
#define rep(i,x) for(int i=0;i<x;i++)
#define repn(i,x) for(int i=1;i<=x;i++)
#define SORT(x) sort(x.begin(),x.end())
#define ERASE(x) x.erase(unique(x.begin(),x.end()),x.end())
#define POSL(x,v) (lower_bound(x.begin(),x.end(),v)-x.begin())
#define POSU(x,v) (upper_bound(x.begin(),x.end(),v)-x.begin())
#define all(x) x.begin(),x.end()
#define si(x) int(x.size())
#define pcnt(x) __builtin_popcountll(x)

#ifdef LOCAL
#define dmp(x) cerr<<__LINE__<<" "<<#x<<" "<<x<<endl
#else
#define dmp(x) void(0)
#endif
 
template<class t,class u> bool chmax(t&a,u b){if(a<b){a=b;return true;}else return false;}
template<class t,class u> bool chmin(t&a,u b){if(b<a){a=b;return true;}else return false;}
 
template<class t> using vc=vector<t>;
 
template<class t,class u>
ostream& operator<<(ostream& os,const pair<t,u>& p){
	return os<<"{"<<p.fi<<","<<p.sc<<"}";
}
 
template<class t> ostream& operator<<(ostream& os,const vc<t>& v){
	os<<"{";
	for(auto e:v)os<<e<<",";
	return os<<"}";
}
 
 //https://codeforces.com/blog/entry/62393
struct custom_hash {
	static uint64_t splitmix64(uint64_t x) {
		// http://xorshift.di.unimi.it/splitmix64.c
		x += 0x9e3779b97f4a7c15;
		x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
		x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
		return x ^ (x >> 31);
	}
 
	size_t operator()(uint64_t x) const {
		static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
		return splitmix64(x + FIXED_RANDOM);
	}
	//don't make x negative!
	size_t operator()(pair<int,int> x)const{
		return operator()(uint64_t(x.first)<<32|x.second);
	}
};
//unordered_set -> dtype, null_type
//unordered_map -> dtype(key), dtype(value)
using namespace __gnu_pbds;
template<class t,class u>
using hash_table=gp_hash_table<t,u,custom_hash>;

template<class T>
void g(T &a){
	cin >> a;
}
template<class T>
void o(const T &a,bool space=false){
	cout << a << (space?' ':'\n');
}
//ios::sync_with_stdio(false);
const ll mod = 998244353;
//const ll mod = 1000000007;
mt19937_64 mt(chrono::steady_clock::now().time_since_epoch().count());
template<class T>
void add(T&a,T b){
	a+=b;
	if(a >= mod) a-=mod;
}
ll modpow(ll x,ll n){
	ll res=1;
	while(n>0){
		if(n&1) res=res*x%mod;
		x=x*x%mod;
		n>>=1;
	}
	return res;
}
#define _sz 400005
ll F[_sz],R[_sz];
void make(){
	F[0] = 1;
	for(int i=1;i<_sz;i++) F[i] = F[i-1]*i%mod;
	R[_sz-1] = modpow(F[_sz-1], mod-2);
	for(int i=_sz-2;i>=0;i--) R[i] = R[i+1] * (i+1) % mod;
}
ll C(int a,int b){
	if(b < 0 || a < b) return 0;
	return F[a]*R[b]%mod*R[a-b]%mod;
}
//o(ans?"Yes":"No");
typedef vector<ll> vi;
vi shrink(vi a){
	while(a.size() && a.back() == 0) a.pop_back();
	return a;
}
vi mul_int(vi a, int M){
	for(auto &b: a) b = (int)((ll)(b) * M) % mod;
	return a;
}
template<const int md>
struct ntt{
	inline void add(int &a, int b) { a += b; if(a >= md) a -= md; }
	inline void sub(int &a, int b) { a -= b; if(a < 0) a += md; }
	inline int add2(int a, int b) { a += b; if(a >= md) a -= md; return a;}
	inline int sub2(int a, int b) { a -= b; if(a < 0) a += md; return a;}
	inline int mul(int a, int b) { return (int)((ll)a*b%md); }
	inline int power(int a, long long b) {
		int res = 1;
		while (b > 0) {
			if (b & 1) res = mul(res, a);
	    	a = mul(a, a);
			b >>= 1;
		}
		return res;
	}
	inline int inv(int a) {
		a %= md;
		if (a < 0) a += md;
		int b = md, u = 0, v = 1;
		while (a) {
			int t = b / a;
			b -= t * a; swap(a, b);
			u -= t * v; swap(u, v);
		}
		assert(b == 1);
		if (u < 0) u += md;
		return u;
	}
	
 	int max_base, root;
	vector<int> dw, idw;
	ntt() {
		int tmp = md - 1;
		max_base = 0;
		while (tmp % 2 == 0) {
			tmp /= 2;
			max_base++;
		}
		root = 2;
		while (power(root, (md-1)>>1) == 1) root++;
		dw.resize(max_base); idw.resize(max_base);
		rep(i, max_base){
			sub(dw[i], power(root, (md-1) >> (i+2)));
			idw[i] = inv(dw[i]);
		}
	}
	void fft(vector<int> &a, bool inv) {
		const int n = a.size();
		assert((n & (n - 1)) == 0);
		assert(__builtin_ctz(n) <= max_base);
		if(!inv){
			for(int m=n;m>>=1;){
				int w = 1;
				for(int s=0,k=0; s<n; s += 2*m){
					for(int i=s, j=s+m ; i < s+m; ++i, ++j) {
						int x = a[i], y = mul(a[j], w);
						a[j] = (x>=y?x-y:x+md-y);
						a[i] = (x+y>=md?x+y-md:x+y);
					}
					w = mul(w, dw[__builtin_ctz(++k)]);
				}
			}
		}
		else{
			for(int m=1;m<n;m*=2){
				int w = 1;
				for(int s=0,k=0; s<n; s += 2*m){
					for(int i=s, j=s+m ; i < s+m; ++i, ++j) {
						int x = a[i], y = a[j];
						a[j] = (x>=y?x-y:x+md-y);
						a[j] = mul(a[j], w);
						a[i] = (x+y>=md?x+y-md:x+y);
					}
					w = mul(w, idw[__builtin_ctz(++k)]);
				}
			}
		}
	}
	vector<int> multiply(vector<int> a, vector<int> b, int eq = 0) {
		int need = a.size() + b.size() - 1;
		int nbase = 0;
		while ((1 << nbase) < need) nbase++;
		int sz = 1 << nbase;
		a.resize(sz);
		b.resize(sz);
		fft(a, 0);
		if (eq) b = a; else fft(b, 0);
		int inv_sz = inv(sz);
		for (int i = 0; i < sz; i++) {
			a[i] = mul(mul(a[i], b[i]), inv_sz);
		}
		fft(a, 1);
		a.resize(need);
		return a;
	}
	vector<int> square(vector<int> a) {
		return multiply(a, a, 1);
	}
};
ntt<998244353>f;
vi mul(vi a, vi b, int eq = 0){
	return f.multiply(a, b, eq);
}
vi add(vi a, vi b,int M=-1){
    if(a.size() < b.size()) swap(a,b);
    for(int i=0;i<b.size();i++){
        a[i]+=b[i];
        if(a[i] < 0) a[i] += mod;
        if(a[i] >= mod) a[i] -= mod;
    }
    if(M >= 0 && a.size() > M) a.resize(M);
    return a;
}
vi sub(vi a, vi b,int M=-1){
    if(a.size() < b.size()) a.resize(b.size(), 0);
    for(int i=0;i<b.size();i++){
        a[i]-=b[i];
        if(a[i] < 0) a[i] += mod;
        if(a[i] >= mod) a[i] -= mod;
    }
    if(M >= 0 && a.size() > M) a.resize(M);
    return a;
}
vi lw(vi a, int x){
	if(a.size() > x) a.resize(x);
	return a;
} 
vi inv(vi a,int M){
	if(a.empty() || a[0] == 0) return vi();
	vi ret(M);
	ret[0] = modpow(a[0],mod-2);
	int cur = 1;
	int nxt = 1;
	while(cur < M){
		auto at = lw(ret, cur);
		ret = sub(add(at, at), mul(mul(at, at, 1), lw(a, cur*2)));
		ret.resize(cur << 1);
		nxt++;
		cur <<= 1;
	}
	assert(ret.size() >= M);
	ret.resize(M);
	return ret;
}
vi modpow(vi a, ll n, vi b){
	vi rb = b;
	reverse(all(rb)); rb = inv(rb, rb.size());
	
	auto get_mod = [&](vi v){
		vi dv, u = v;
		if(v.size() < b.size()) dv = {};
		else{
			int sz = v.size() - b.size() + 1;
			vi y = lw(rb, sz);
			reverse(all(v)); v = lw(v, sz);
			dv = mul(v, y);
			dv.resize(sz);
			reverse(all(dv));
		}
		u = sub(u, mul(dv, b));
		return shrink(u);
	};
	if(a.size() >= b.size()){
		a = get_mod(a);
	}
	assert(a.size() < b.size());
	vi ret = {1};
	while(n){
		if(n & 1){
			ret = mul(ret, a);
			ret = get_mod(ret);
		}
		n >>= 1;
		a = mul(a, a, 1);
		a = get_mod(a);
	}
	return ret;
}
vector<ll>BerlekampMassey(vector<ll>x){
	vector<ll>ls,cur;
	int lf,ld;
	rep(i,x.size()){
		ll t = 0;
		for(int j=0;j<cur.size();j++){
			t = (t+x[i-j-1]*cur[j])%mod;
		}
		if( ((t-x[i])%mod+mod)%mod == 0 ) continue;
		if(!cur.size()){
			cur.resize(i+1); lf = i; ld = (t-x[i])%mod;
			continue;
		}
		ll k = -(x[i]-t)*modpow(ld,mod-2)%mod;
		vector<ll>c(i-lf-1);
		c.pb(k);
		rep(j,ls.size()) c.pb(-ls[j]*k%mod);
		if(c.size() < cur.size()) c.resize(cur.size());
		rep(j,cur.size()){
			c[j]=(c[j]+cur[j])%mod;
		}
		if(i-lf+(int)(ls.size()) >= (int)(cur.size())){
			ls = cur, lf = i, ld = (t-x[i])%mod;
		}
		cur = c;
	}
	rep(i,cur.size()) cur[i] = (cur[i]%mod+mod)%mod;
	return cur;
}

//numは線形漸化的な列、特定に十分な長さがあるものとする (ない場合どうなるかは、不明)
//0-indexed でn番目を返す
ll calc_linear_nth(vector<ll>num, ll n){
	if(num.size() > n) return num[n];
	auto rel = BerlekampMassey(num);
	//本当に特定できてるか知りたいなら、numを"""十分"""長くとった上で
	//assert(rel.size()*2+2 < num.size());
	for(auto &at:rel) {
		if(at) at = mod - at;
	}
	reverse(all(rel));
	rel.pb(1);
	auto ans = modpow({0, 1}, n, rel);
	ll ret = 0;
	rep(i, ans.size()){
		ret += 1LL*ans[i]*num[i]%mod;
	}
	return (ret%mod+mod)%mod;
}
int n, m, dp[2][105][105];
void solve(){
	cin >> n >> m; if(m==1){o(0);return;}
	for(int i=1;i<=m;i++) dp[0][i][1%i] = 1;
	int cur = 0, nxt = 1;
	vc<int>ans;
	rep(i, 10500){
		memset(dp[nxt], 0, sizeof(dp[nxt]));
		vc<int>tmp(105, 0);
		int A = 0;
		rep(a, 105) repn(b, 104) if(dp[cur][a][b]) {
			add(tmp[a], dp[cur][a][b]);
			add(A     , dp[cur][a][b]);
		}
		ans.pb(A);
		
		repn(j, m){
			//j -> j
			rep(x, j) add(dp[nxt][j][(x+1)%j], dp[cur][j][x]);
			//other -> j
			add(dp[nxt][j][1%j], (A+mod-tmp[j])%mod);
		}
		
		swap(cur, nxt);
	}
	o(calc_linear_nth(ans, n-1));
}
signed main(){
	cin.tie(0);
	ios::sync_with_stdio(0);
	cout<<fixed<<setprecision(20);
	int t; t = 1; //cin >> t;
	while(t--) solve();
}
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