結果
| 問題 | No.1889 K Consecutive Ks (Hard) |
| ユーザー |
 Sumitacchan
|
| 提出日時 | 2022-03-25 23:14:39 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 3,529 ms / 6,000 ms |
| コード長 | 9,244 bytes |
| コンパイル時間 | 2,208 ms |
| コンパイル使用メモリ | 208,536 KB |
| 最終ジャッジ日時 | 2025-01-28 12:32:55 |
|
ジャッジサーバーID （参考情報） |
judge4 / judge3 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 22 |
ソースコード
#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 1000000000000000000template<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 debugusing 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() - 1vector<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;}