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 #
プレゼンテーションモードにする

//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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