結果

問題 No.1889 K Consecutive Ks (Hard)
ユーザー SumitacchanSumitacchan
提出日時 2022-03-25 23:14:39
言語 C++17
(gcc 13.2.0 + boost 1.83.0)
結果
AC  
実行時間 3,785 ms / 6,000 ms
コード長 9,244 bytes
コンパイル時間 2,746 ms
コンパイル使用メモリ 210,588 KB
実行使用メモリ 37,424 KB
最終ジャッジ日時 2024-04-22 08:10:51
合計ジャッジ時間 53,699 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge5
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 2 ms
6,812 KB
testcase_01 AC 2 ms
6,940 KB
testcase_02 AC 3,703 ms
37,276 KB
testcase_03 AC 2 ms
6,940 KB
testcase_04 AC 2 ms
6,940 KB
testcase_05 AC 2 ms
6,940 KB
testcase_06 AC 2 ms
6,944 KB
testcase_07 AC 2 ms
6,940 KB
testcase_08 AC 2 ms
6,940 KB
testcase_09 AC 3,728 ms
36,476 KB
testcase_10 AC 3,773 ms
37,184 KB
testcase_11 AC 697 ms
12,696 KB
testcase_12 AC 1,601 ms
20,488 KB
testcase_13 AC 1,580 ms
19,352 KB
testcase_14 AC 1,606 ms
21,216 KB
testcase_15 AC 3,755 ms
33,584 KB
testcase_16 AC 3,785 ms
36,568 KB
testcase_17 AC 1,558 ms
17,676 KB
testcase_18 AC 3,741 ms
35,436 KB
testcase_19 AC 3,732 ms
36,736 KB
testcase_20 AC 3,713 ms
37,424 KB
testcase_21 AC 3,684 ms
37,300 KB
testcase_22 AC 3,684 ms
37,344 KB
testcase_23 AC 1,589 ms
21,728 KB
testcase_24 AC 3,703 ms
37,348 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

#include <bits/stdc++.h>
using namespace std;
//using namespace atcoder;
struct fast_ios { fast_ios(){ cin.tie(0); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_;
#define FOR(i, begin, end) for(int i=(begin);i<(end);i++)
#define REP(i, n) FOR(i,0,n)
#define IFOR(i, begin, end) for(int i=(end)-1;i>=(begin);i--)
#define IREP(i, n) IFOR(i,0,n)
#define Sort(v) sort(v.begin(), v.end())
#define Reverse(v) reverse(v.begin(), v.end())
#define all(v) v.begin(),v.end()
#define SZ(v) ((int)v.size())
#define Lower_bound(v, x) distance(v.begin(), lower_bound(v.begin(), v.end(), x))
#define Upper_bound(v, x) distance(v.begin(), upper_bound(v.begin(), v.end(), x))
#define chmax(a, b) a = max(a, b)
#define chmin(a, b) a = min(a, b)
#define bit(n) (1LL<<(n))
#define debug(x) cout << #x << "=" << x << endl;
#define vdebug(v) { cout << #v << "=" << endl; REP(i_debug, (int)v.size()){ cout << v[i_debug] << ","; } cout << endl; }
#define mdebug(m) { cout << #m << "=" << endl; REP(i_debug, (int)m.size()){ REP(j_debug, (int)m[i_debug].size()){ cout << m[i_debug][j_debug] << ","; } cout << endl;} }
#define pb push_back
#define fi first
#define se second
#define int long long
#define INF 1000000000000000000
template<typename T> istream &operator>>(istream &is, vector<T> &v){ for (auto &x : v) is >> x; return is; }
template<typename T> ostream &operator<<(ostream &os, vector<T> &v){ for(int i = 0; i < (int)v.size(); i++) { cout << v[i]; if(i != (int)v.size() - 1) cout << endl; }; return os; }
template<typename T1, typename T2> ostream &operator<<(ostream &os, pair<T1, T2> p){ cout << '(' << p.first << ',' << p.second << ')'; return os; }
template<typename T> void Out(T x) { cout << x << endl; }
template<typename T1, typename T2> void chOut(bool f, T1 y, T2 n) { if(f) Out(y); else Out(n); }

using vec = vector<int>;
using mat = vector<vec>;
using Pii = pair<int, int>;
using v_bool = vector<bool>;
using v_Pii = vector<Pii>;

//int dx[4] = {1,0,-1,0};
//int dy[4] = {0,1,0,-1};
//char d[4] = {'D','R','U','L'};

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

template<long long MOD>
struct ModInt{

    using ll = long long;
    ll val;

    void setval(ll v) { val = v % MOD; };
    ModInt(): val(0) {}
    ModInt(ll v) { setval(v); };

    ModInt operator+(const ModInt &x) const { return ModInt(val + x.val); }
    ModInt operator-(const ModInt &x) const { return ModInt(val - x.val + MOD); }
    ModInt operator*(const ModInt &x) const { return ModInt(val * x.val); }
    ModInt operator/(const ModInt &x) const { return *this * x.inv(); }
    ModInt operator-() const { return ModInt(MOD - val); }
    ModInt operator+=(const ModInt &x) { return *this = *this + x; }
    ModInt operator-=(const ModInt &x) { return *this = *this - x; }
    ModInt operator*=(const ModInt &x) { return *this = *this * x; }
    ModInt operator/=(const ModInt &x) { return *this = *this / x; }
    bool operator==(const ModInt &x) const { return (*this).val == x.val; }

    friend ostream& operator<<(ostream &os, const ModInt &x) { os << x.val; return os; }
    friend istream& operator>>(istream &is, ModInt &x) { is >> x.val; x.val = (x.val % MOD + MOD) % MOD; return is; }

    ModInt pow(ll n) const {
        ModInt a = 1;
        if(n == 0) return a;
        int i0 = 64 - __builtin_clzll(n);
        for(int i = i0 - 1; i >= 0; i--){
            a = a * a;
            if((n >> i) & 1) a *= (*this); 
        }
        return a;
    }
    ModInt inv() const { return this->pow(MOD - 2); }
};

using mint = ModInt<mod>; mint pow(mint x, long long n) { return x.pow(n); }
//using mint = double; //for debug
using mvec = vector<mint>;
using mmat = vector<mvec>;

struct Combination{

    vector<mint> fact, invfact;

    Combination(int N){
        fact = vector<mint>({mint(1)});
        invfact = vector<mint>({mint(1)});
        fact_initialize(N);
    }

    void fact_initialize(int N){
        int i0 = fact.size();
        if(i0 >= N + 1) return;
        fact.resize(N + 1);
        invfact.resize(N + 1);
        for(int i = i0; i <= N; i++) fact[i] = fact[i - 1] * i;
        invfact[N] = (mint)1 / fact[N];
        for(int i = N - 1; i >= i0; i--) invfact[i] = invfact[i + 1] * (i + 1); 
    }

    mint nCr(int n, int r){
        if(n < 0 || r < 0 || r > n) return mint(0);
        if((int)fact.size() < n + 1) fact_initialize(n);
        return fact[n] * invfact[r] * invfact[n - r];
    }

    mint nPr(int n, int r){
        if(n < 0 || r < 0 || r > n) return mint(0);
        if((int)fact.size() < n + 1) fact_initialize(n);
        return fact[n] * invfact[n - r];
    }

    mint Catalan(int n){
        if(n < 0) return 0;
        else if(n == 0) return 1;
        if((int)fact.size() < 2 * n + 1) fact_initialize(2 * n);
        return fact[2 * n] * invfact[n + 1] * invfact[n];
    }

};

template<long long MOD>
struct NTT
{
    using ll = long long;
    int MAX_LOGN;
    ll e;
    vector<vector<ll>> W;

    NTT(){
        if(MOD == 924844033) e = 5;
        else if(MOD == 998244353) e = 3;
        else if(MOD == 1012924417) e = 5;
        else assert(false);

        assert(MOD > 1); 
        MAX_LOGN = __builtin_ffsll(MOD - 1) - 1;
        W.resize(MAX_LOGN + 1);
    }

    ll modpow(ll x, ll n) {
        ll a = 1;
        if(n == 0) return a;
        int i0 = 64 - __builtin_clzll(n);
        for(int i = i0 - 1; i >= 0; i--){
            (a *= a) %= MOD;
            if((n >> i) & 1) (a *= x) %= MOD;
        }
        return a;
    }

    void init_W(int n){
        W[n].resize((1 << n) + 1);
        ll w0 = modpow(e, (MOD - 1) >> n);
        W[n][0] = 1;
        for(int i = 1; i < (int)W[n].size(); i++){
            W[n][i] = (W[n][i - 1] * w0) % MOD;
        }
    }

    void bit_reverse(vector<ll> &f){
        int N = f.size();
        for(int i = 1, j = 0; i < N; i++){
            for(int k = (N >> 1); ((j ^= k) & k) == 0; k >>= 1);
            if(i < j) swap(f[i], f[j]);
        }
    }

    void fft(vector<ll> &f){
        int N = f.size();
        int n = 31 - __builtin_clz((signed)N);
        assert(N == (1 << n));
        assert(n <= MAX_LOGN);

        if(W[n].size() == 0) init_W(n);

        for(int k = n - 1; k >= 0; k--){
            for(int i = 0; i < (1 << (n - 1 - k)); i++){
                for(int j = 0; j < (1 << k); j++){
                    int u = (i << (k + 1)) + j;
                    int v = u | (1 << k);
                    ll fu = f[u], fv = f[v];
                    f[u] = fu + fv;
                    if(f[u] >= MOD) f[u] -= MOD;
                    f[v] = ((fu - fv + MOD) * W[n][j << (n - 1 - k)]) % MOD;
                }
            }
        }
        bit_reverse(f);
    }

    void ifft(vector<ll> &f){
        int N = f.size();
        int n = 31 - __builtin_clz((signed)N);
        assert(N == (1 << n));
        assert(n <= MAX_LOGN);

        if(W[n].size() == 0) init_W(n);

        for(int k = n - 1; k >= 0; k--){
            for(int i = 0; i < (1 << (n - 1 - k)); i++){
                for(int j = 0; j < (1 << k); j++){
                    int u = (i << (k + 1)) + j;
                    int v = u | (1 << k);
                    ll fu = f[u], fv = f[v];
                    f[u] = fu + fv;
                    if(f[u] >= MOD) f[u] -= MOD;
                    f[v] = ((fu - fv + MOD) * W[n][N - (j << (n - 1 - k))]) % MOD;
                }
            }
        }

        ll inv = modpow(N, MOD - 2);
        for(int i = 0; i < N; i++) (f[i] *= inv) %= MOD;
        bit_reverse(f);
    }

    // if adjust_size is true, the array size of the result becomes A.size() + B.size() - 1
    vector<ll> convolution(vector<ll> A, vector<ll> B, bool adjust_size = true){
        int sA = A.size(), sB = B.size();
        if(adjust_size){
            int N = 1;
            while(sA + sB - 1 > N) N <<= 1;
            A.resize(N);
            B.resize(N);
        }else{
            assert(sA == sB);
        }
        fft(A);
        fft(B);

        int N = A.size();
        vector<ll> C(N);
        for(int i = 0; i < N; i++) C[i] = (A[i] * B[i]) % MOD;
        ifft(C);
        if(adjust_size) C.resize(sA + sB - 1);

        return C;
    }

    vector<ModInt<MOD>> convolution(vector<ModInt<MOD>> A, vector<ModInt<MOD>> B, bool adjust_size = true){
        vector<ll> A_(A.size()), B_(B.size());
        for(int i = 0; i < (int)A.size(); i++) A_[i] = A[i].val;
        for(int i = 0; i < (int)B.size(); i++) B_[i] = B[i].val;
        auto C_ = convolution(A_, B_, adjust_size);
        vector<ModInt<MOD>> C(C_.size());
        for(int i = 0; i < (int)C_.size(); i++) C[i] = C_[i];
        return C;
    }

};

signed main(){

    int N, M; cin >> N >> M;
    NTT<mod> ntt;

    mvec f(N + 1);
    f[1] = M - 1;
    FOR(m, 2, M + 1){
        for(int n = m; n <= N; n += m){
            f[n] -= 1;
            if(n + 1 <= N) f[n + 1] += 1;
        }
    }
    //vdebug(f);
    mvec S(N + 1);
    S[0] = 1;
    // (f,S)->(f^2,(1+f)S)
    REP(t, 20){
        f[0] += 1;
        S = ntt.convolution(f, S);
        S.resize(N + 1);
        f[0] -= 1;
        f = ntt.convolution(f, f);
        f.resize(N + 1);
    }
    //vdebug(f); vdebug(S);
    mint ans = pow((mint)M, N) - S[N];
    Out(ans);

    return 0;
}
0