結果
問題 | No.1962 Not Divide |
ユーザー |
![]() |
提出日時 | 2022-05-27 22:41:18 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 559 ms / 2,000 ms |
コード長 | 18,087 bytes |
コンパイル時間 | 2,555 ms |
コンパイル使用メモリ | 217,268 KB |
最終ジャッジ日時 | 2025-01-29 16:09:46 |
ジャッジサーバーID (参考情報) |
judge4 / judge5 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 21 |
ソースコード
#include <bits/stdc++.h>using namespace std;using ll = long long;using uint = unsigned int;using ull = unsigned long long;#define rep(i,n) for(int i=0;i<int(n);i++)#define rep1(i,n) for(int i=1;i<=int(n);i++)#define per(i,n) for(int i=int(n)-1;i>=0;i--)#define per1(i,n) for(int i=int(n);i>0;i--)#define all(c) c.begin(),c.end()#define si(x) int(x.size())#define pb push_back#define eb emplace_back#define fs first#define sc secondtemplate<class T> using V = vector<T>;template<class T> using VV = vector<vector<T>>;template<class T,class U> bool chmax(T& x, U y){if(x<y){ x=y; return true; }return false;}template<class T,class U> bool chmin(T& x, U y){if(y<x){ x=y; return true; }return false;}template<class T> void mkuni(V<T>& v){sort(all(v));v.erase(unique(all(v)),v.end());}template<class T> int lwb(const V<T>& v, const T& a){return lower_bound(all(v),a) - v.begin();}template<class T>V<T> Vec(size_t a) {return V<T>(a);}template<class T, class... Ts>auto Vec(size_t a, Ts... ts) {return V<decltype(Vec<T>(ts...))>(a, Vec<T>(ts...));}template<class S,class T> ostream& operator<<(ostream& o,const pair<S,T> &p){return o<<"("<<p.fs<<","<<p.sc<<")";}template<class T> ostream& operator<<(ostream& o,const vector<T> &vc){o<<"{";for(const T& v:vc) o<<v<<",";o<<"}";return o;}constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n-1); }#ifdef LOCAL#define show(x) cerr << "LINE" << __LINE__ << " : " << #x << " = " << (x) << endlvoid dmpr(ostream& os){os<<endl;}template<class T,class... Args>void dmpr(ostream&os,const T&t,const Args&... args){os<<t<<" ~ ";dmpr(os,args...);}#define shows(...) cerr << "LINE" << __LINE__ << " : ";dmpr(cerr,##__VA_ARGS__)#define dump(x) cerr << "LINE" << __LINE__ << " : " << #x << " = {"; \for(auto v: x) cerr << v << ","; cerr << "}" << endl;#else#define show(x) void(0)#define dump(x) void(0)#define shows(...) void(0)#endiftemplate<class D> D divFloor(D a, D b){return a / b - (((a ^ b) < 0 && a % b != 0) ? 1 : 0);}template<class D> D divCeil(D a, D b) {return a / b + (((a ^ b) > 0 && a % b != 0) ? 1 : 0);}/*2021/04/14 大幅変更poly 基本, MultipointEval, Interpolate*/template<unsigned int mod_>struct ModInt{using uint = unsigned int;using ll = long long;using ull = unsigned long long;constexpr static uint mod = mod_;uint v;ModInt():v(0){}ModInt(ll _v):v(normS(_v%mod+mod)){}explicit operator bool() const {return v!=0;}static uint normS(const uint &x){return (x<mod)?x:x-mod;} // [0 , 2*mod-1] -> [0 , mod-1]static ModInt make(const uint &x){ModInt m; m.v=x; return m;}ModInt operator+(const ModInt& b) const { return make(normS(v+b.v));}ModInt operator-(const ModInt& b) const { return make(normS(v+mod-b.v));}ModInt operator-() const { return make(normS(mod-v)); }ModInt operator*(const ModInt& b) const { return make((ull)v*b.v%mod);}ModInt operator/(const ModInt& b) const { return *this*b.inv();}ModInt& operator+=(const ModInt& b){ return *this=*this+b;}ModInt& operator-=(const ModInt& b){ return *this=*this-b;}ModInt& operator*=(const ModInt& b){ return *this=*this*b;}ModInt& operator/=(const ModInt& b){ return *this=*this/b;}ModInt& operator++(int){ return *this=*this+1;}ModInt& operator--(int){ return *this=*this-1;}template<class T> friend ModInt operator+(T a, const ModInt& b){ return (ModInt(a) += b);}template<class T> friend ModInt operator-(T a, const ModInt& b){ return (ModInt(a) -= b);}template<class T> friend ModInt operator*(T a, const ModInt& b){ return (ModInt(a) *= b);}template<class T> friend ModInt operator/(T a, const ModInt& b){ return (ModInt(a) /= b);}ModInt pow(ll p) const {if(p<0) return inv().pow(-p);ModInt a = 1;ModInt x = *this;while(p){if(p&1) a *= x;x *= x;p >>= 1;}return a;}ModInt inv() const { // should be primereturn pow(mod-2);}// ll extgcd(ll a,ll b,ll &x,ll &y) const{// ll p[]={a,1,0},q[]={b,0,1};// while(*q){// ll t=*p/ *q;// rep(i,3) swap(p[i]-=t*q[i],q[i]);// }// if(p[0]<0) rep(i,3) p[i]=-p[i];// x=p[1],y=p[2];// return p[0];// }// ModInt inv() const {// ll x,y;// extgcd(v,mod,x,y);// return make(normS(x+mod));// }bool operator==(const ModInt& b) const { return v==b.v;}bool operator!=(const ModInt& b) const { return v!=b.v;}bool operator<(const ModInt& b) const { return v<b.v;}friend istream& operator>>(istream &o,ModInt& x){ll tmp;o>>tmp;x=ModInt(tmp);return o;}friend ostream& operator<<(ostream &o,const ModInt& x){ return o<<x.v;}};using mint = ModInt<998244353>;//using mint = ModInt<1000000007>;V<mint> fact,ifact,invs;mint Choose(int a,int b){if(b<0 || a<b) return 0;return fact[a] * ifact[b] * ifact[a-b];}void InitFact(int N){ //[0,N]N++;fact.resize(N);ifact.resize(N);invs.resize(N);fact[0] = 1;rep1(i,N-1) fact[i] = fact[i-1] * i;ifact[N-1] = fact[N-1].inv();for(int i=N-2;i>=0;i--) ifact[i] = ifact[i+1] * (i+1);rep1(i,N-1) invs[i] = fact[i-1] * ifact[i];}// inplace_fmt (without bit rearranging)// fft:// a[rev(i)] <- \sum_j \zeta^{ij} a[j]// invfft:// a[i] <- (1/n) \sum_j \zeta^{-ij} a[rev(j)]// These two are inversions.// !!! CHANGE IF MOD is unusual !!!const int ORDER_2_MOD_MINUS_1 = 23; // ord_2 (mod-1)const mint PRIMITIVE_ROOT = 3; // primitive root of (Z/pZ)*void fft(V<mint>& a){static constexpr uint mod = mint::mod;static constexpr uint mod2 = mod + mod;static const int H = ORDER_2_MOD_MINUS_1;static const mint root = PRIMITIVE_ROOT;static mint magic[H-1];int n = si(a);assert(!(n & (n-1))); assert(n >= 1); assert(n <= 1<<H); // n should be power of 2if(!magic[0]){ // precalcrep(i,H-1){mint w = -root.pow(((mod-1)>>(i+2))*3);magic[i] = w;}}int m = n;if(m >>= 1){rep(i,m){uint v = a[i+m].v; // < Ma[i+m].v = a[i].v + mod - v; // < 2Ma[i].v += v; // < 2M}}if(m >>= 1){mint p = 1;for(int h=0,s=0; s<n; s += m*2){for(int i=s;i<s+m;i++){uint v = (a[i+m] * p).v; // < Ma[i+m].v = a[i].v + mod - v; // < 3Ma[i].v += v; // < 3M}p *= magic[__builtin_ctz(++h)];}}while(m){if(m >>= 1){mint p = 1;for(int h=0,s=0; s<n; s += m*2){for(int i=s;i<s+m;i++){uint v = (a[i+m] * p).v; // < Ma[i+m].v = a[i].v + mod - v; // < 4Ma[i].v += v; // < 4M}p *= magic[__builtin_ctz(++h)];}}if(m >>= 1){mint p = 1;for(int h=0,s=0; s<n; s += m*2){for(int i=s;i<s+m;i++){uint v = (a[i+m] * p).v; // < Ma[i].v = (a[i].v >= mod2) ? a[i].v - mod2 : a[i].v; // < 2Ma[i+m].v = a[i].v + mod - v; // < 3Ma[i].v += v; // < 3M}p *= magic[__builtin_ctz(++h)];}}}rep(i,n){a[i].v = (a[i].v >= mod2) ? a[i].v - mod2 : a[i].v; // < 2Ma[i].v = (a[i].v >= mod) ? a[i].v - mod : a[i].v; // < M}// finally < mod !!}void invfft(V<mint>& a){static constexpr uint mod = mint::mod;static constexpr uint mod2 = mod + mod;static const int H = ORDER_2_MOD_MINUS_1;static const mint root = PRIMITIVE_ROOT;static mint magic[H-1];int n = si(a);assert(!(n & (n-1))); assert(n >= 1); assert(n <= 1<<H); // n should be power of 2if(!magic[0]){ // precalcrep(i,H-1){mint w = -root.pow(((mod-1)>>(i+2))*3);magic[i] = w.inv();}}int m = 1;if(m < n>>1){mint p = 1;for(int h=0,s=0; s<n; s += m*2){for(int i=s;i<s+m;i++){ull x = a[i].v + mod - a[i+m].v; // < 2Ma[i].v += a[i+m].v; // < 2Ma[i+m].v = (p.v * x) % mod; // < M}p *= magic[__builtin_ctz(++h)];}m <<= 1;}for(;m < n>>1; m <<= 1){mint p = 1;for(int h=0,s=0; s<n; s+= m*2){for(int i=s;i<s+(m>>1);i++){ull x = a[i].v + mod2 - a[i+m].v; // < 4Ma[i].v += a[i+m].v; // < 4Ma[i].v = (a[i].v >= mod2) ? a[i].v - mod2 : a[i].v; // < 2Ma[i+m].v = (p.v * x) % mod; // < M}for(int i=s+(m>>1); i<s+m; i++){ull x = a[i].v + mod - a[i+m].v; // < 2Ma[i].v += a[i+m].v; // < 2Ma[i+m].v = (p.v * x) % mod; // < M}p *= magic[__builtin_ctz(++h)];}}if(m < n){rep(i,m){uint x = a[i].v + mod2 - a[i+m].v; // < 4Ma[i].v += a[i+m].v; // < 4Ma[i+m].v = x; // < 4M}}const mint in = mint(n).inv();rep(i,n) a[i] *= in; // < M// finally < mod !!}// A,B = 500000 -> 70ms// verify https://judge.yosupo.jp/submission/44937V<mint> multiply(V<mint> a, V<mint> b) {int A = si(a), B = si(b);if (!A || !B) return {};int n = A+B-1;int s = 1; while(s<n) s*=2;if(a == b){ // # of fft call : 3 -> 2a.resize(s); fft(a);rep(i,s) a[i] *= a[i];}else{a.resize(s); fft(a);b.resize(s); fft(b);rep(i,s) a[i] *= b[i];}invfft(a); a.resize(n);return a;}/*係数アクセスf[i] でいいが、 配列外参照する可能性があるなら at/set*/template<class mint>struct Poly: public V<mint>{template<class...Args>Poly(Args...args) : V<mint>(args...){}Poly(initializer_list<mint> li) : V<mint>(li){}int size() const { return V<mint>::size(); }mint at(int i) const {return i<size() ? (*this)[i] : 0;}void set(int i, mint x){if(i>=size() && !x) return;while(i>=size()) this->pb(0);(*this)[i] = x;return;}mint operator()(mint x) const { // evalmint res = 0;int n = size();mint a = 1;rep(i,n){res += a * (*this)[i];a *= x;}return res;}Poly low(int n) const { // ignore x^n (take first n), but not emptyreturn Poly(this->begin(), this->begin()+min(max(n,1),size()));}Poly rev() const {return Poly(this->rbegin(), this->rend());}friend ostream& operator<<(ostream &o,const Poly& f){o << "[";rep(i,f.size()){o << f[i];if(i != f.size()-1) o << ",";}o << "]";return o;}Poly operator-() const {Poly res = *this;for(auto& v: res) v = -v;return res;}template<class T>Poly& operator+=(T c){(*this)[0] += c;return *this;}template<class T>Poly& operator-=(T c){(*this)[0] -= c;return *this;}template<class T>Poly& operator*=(T c){for(auto& v: *this) v *= c;return *this;}template<class T>Poly& operator/=(T c){return *this *= mint(1)/mint(c);}Poly& operator+=(const Poly& r){if(size() < r.size()) this->resize(r.size(),0);rep(i,r.size()) (*this)[i] += r[i];return *this;}Poly& operator-=(const Poly& r){if(size() < r.size()) this->resize(r.size(),0);rep(i,r.size()) (*this)[i] -= r[i];return *this;}Poly& operator*=(const Poly& r){return *this = multiply(*this,r);}// 何回も同じrで割り算するなら毎回rinvを計算するのは無駄なので、呼び出し側で一回計算した後直接こっちを呼ぶと良い// 取るべきinvの長さに注意// 例えば mod r で色々計算したい時は、基本的に deg(r) * 2 長さの多項式を r で割ることになる// とはいえいったん rinv を長く計算したらより短い場合はprefix見るだけだし、 rinv としてムダに長いものを渡しても問題ないので// 割られる多項式として最大の次数を取ればよいPoly quotient(const Poly& r, const Poly& rinv){int m = r.size(); assert(r[m-1].v);int n = size();int s = n-m+1;if(s <= 0) return {0};return (rev().low(s)*rinv.low(s)).low(s).rev();}Poly& operator/=(const Poly& r){return *this = quotient(r,r.rev().inv(max(size()-r.size(),0)+1));}Poly& operator%=(const Poly& r){*this -= *this/r * r;return *this = low(r.size()-1);}template<class T> Poly operator+(T c) const {return Poly(*this) += c; }template<class T> Poly operator-(T c) const {return Poly(*this) -= c; }template<class T> Poly operator*(T c) const {return Poly(*this) *= c; }template<class T> Poly operator/(T c) const {return Poly(*this) /= c; }Poly operator+(const Poly& r) const {return Poly(*this) += r; }Poly operator-(const Poly& r) const {return Poly(*this) -= r; }Poly operator*(const Poly& r) const {return Poly(*this) *= r; }Poly operator/(const Poly& r) const {return Poly(*this) /= r; }Poly operator%(const Poly& r) const {return Poly(*this) %= r; }Poly diff() const {Poly g(max(size()-1,0));rep(i,g.size()) g[i] = (*this)[i+1] * (i+1);return g;}Poly intg() const {assert(si(invs) > size());Poly g(size()+1);rep(i,size()) g[i+1] = (*this)[i] * invs[i+1];return g;}Poly square() const {return multiply(*this,*this);}// 1/f(x) mod x^s// N = s = 500000 -> 90ms// inv は 5 回 fft(2n) を呼んでいるので、multiply が 3 回 fft(2n) を呼ぶのと比べると// だいたい multiply の 5/3 倍の時間がかかる// 導出: Newton// fg = 1 mod x^m// (fg-1)^2 = 0 mod x^2m// f(2g-fg^2) = 1 mod x^2m// verify: https://judge.yosupo.jp/submission/44938Poly inv(int s) const {Poly r(s);r[0] = mint(1)/at(0);for(int n=1;n<s;n*=2){ // 5 times fft : length 2nV<mint> f = low(2*n); f.resize(2*n);fft(f);V<mint> g = r.low(2*n); g.resize(2*n);fft(g);rep(i,2*n) f[i] *= g[i];invfft(f);rep(i,n) f[i] = 0;fft(f);rep(i,2*n) f[i] *= g[i];invfft(f);for(int i=n;i<min(2*n,s);i++) r[i] -= f[i];}return r;}// log f mod x^s// 導出: D log(f) = (D f) / f// 500000: 180ms// mult の 8/3 倍// verify: https://judge.yosupo.jp/submission/44962Poly log(int s) const {assert(at(0) == 1);if(s == 1) return {0};return (low(s).diff() * inv(s-1)).low(s-1).intg();}// e^f mod x^s// f.log(s).exp(s) == [1,0,...,0]// 500000 : 440ms// TODO: 高速化!// 速い実装例 (hos): https://judge.yosupo.jp/submission/36732 150ms// 導出 Newton:// g = exp(f)// log(g) - f = 0// g == g0 mod x^m// g == g0 - (log(g0) - f) / (1/g0) mod x^2m// verify: yosupoPoly exp(int s) const {assert(at(0) == 0);Poly f({1}),g({1});for(int n=1;n<s;n*=2){g = (g*2-g.square().low(n)*f).low(n);Poly q = low(n).diff();q = q + g * (f.diff() - f*q).low(2*n-1);f = (f + f * (low(2*n)-q.intg()) ).low(2*n);}return f.low(s);}// f^p mod x^s// 500000: 600ms// 導出: f^p = e^(p log f)// log 1回、 exp 1回// Exp.cpp (Mifafa technique) も参照// c.f. (f の non0 coef の個数) * s// verify: https://judge.yosupo.jp/submission/44992Poly pow(ll p, int s) const {if(p == 0){return Poly(s) + 1; // 0^0 is 1}int ord = 0;while(ord<s && !at(ord)) ord++;if((s-1)/p < ord) return Poly(s); // s <= p * ordint off = p*ord;int s_ = s-off;const mint a0 = at(ord), ia0 = a0.inv(), ap = a0.pow(p);Poly f(s_); rep(i,s_) f[i] = at(i+ord) * ia0;f = (f.log(s_) * p).exp(s_);Poly res(s);rep(i,s_) res[i+off] = f[i] * ap;return res;}// f^(1/2) mod x^s// f[0] should be 1// 11/6// verify: https://judge.yosupo.jp/submission/44997Poly sqrt(int s) const {assert(at(0) == 1);static const mint i2 = mint(2).inv();V<mint> f{1},g{1},z{1};for(int n=1;n<s;n*=2){rep(i,n) z[i] *= z[i];invfft(z);V<mint> d(2*n);rep(i,n) d[n+i] = z[i] - at(i) - at(n+i);fft(d);V<mint> g2(2*n);rep(i,n) g2[i] = g[i];fft(g2);rep(i,n*2) d[i] *= g2[i];invfft(d);f.resize(n*2);for(int i=n;i<n*2;i++) f[i] = -d[i] * i2;if(n*2 >= s) break;z = f;fft(z);V<mint> eps = g2;rep(i,n*2) eps[i] *= z[i];invfft(eps);rep(i,n) eps[i] = 0;fft(eps);rep(i,n*2) eps[i] *= g2[i];invfft(eps);g.resize(n*2);for(int i=n;i<n*2;i++) g[i] -= eps[i];}f.resize(s);return f;}};// [x^p] f/g// O(n logn logp)// O(f logf + g logg logn) (f が大きくてもややOK)// verified: https://ac.nowcoder.com/acm/contest/11259/H// hos,divAt : https://ac.nowcoder.com/acm/contest/view-submission?submissionId=48462458template<class T>T divAt(Poly<T> f, Poly<T> g, ll p){assert(g.at(0));while(p){auto gm = g;for(int i=1;i<si(g);i+=2) gm[i] = -gm[i];auto f2 = f*gm;auto g2 = g*gm;f.clear();g.clear();for(int i=p&1;i<si(f2);i+=2) f.set(i/2,f2[i]);for(int i=0;i<si(g2);i+=2) g.set(i/2,g2[i]);p /= 2;}return f.at(0)/g.at(0);}/*input:はじめ d 項: a_0, a_1, .., a_{d-1}d+1 項 reccurence: c_0 * a_{i+d} + .. + c_d * a_i = 0aを無駄に与えても良い(足りないと、カス)ll koutput:a_kO(d logd logk)verified: https://judge.yosupo.jp/problem/find_linear_recurrence*/template<class T>T linearRecurrenceAt(V<T> a, V<T> c, ll k){assert(!c.empty() && c[0]);int d = si(c) - 1;assert(si(a) >= d);return divAt((Poly<T>(a.begin(),a.begin()+d) * Poly<T>(c)).low(d), Poly<T>(c), k);}template<class D>Poly<D> berlekamp_massey(const vector<D> &u){int N = u.size();vector<D> b = {D(-1)}, c = {D(-1)};D y = D(1);rep1(n,N){int L = c.size(), M = b.size();D x = 0;rep(i,L) x += c[i]*u[n-L+i];b.pb(0);M++;if(!x) continue;D coef = x/y;if(L<M){auto tmp = c;c.insert(begin(c),M-L,D(0));rep(i,M) c[M-1-i] -= coef*b[M-1-i];b=tmp;y=x;}else{rep(i,M) c[L-1-i] -= coef*b[M-1-i];}}return Poly<D>(c);}mint dp[101][101];mint nx[101][101];int main(){cin.tie(0);ios::sync_with_stdio(false); //DON'T USE scanf/printf/puts !!cout << fixed << setprecision(20);int N,M; cin >> N >> M;auto brute = [&](int N){V<mint> f(N);rep(i,N){if(i == 0){for(int m=2;m<=M;m++) nx[m][1] = 1;}else{mint off = 0;for(int m=2;m<=M;m++) rep(r,m) if(dp[m][r]){nx[m][(r+1)%m] += dp[m][r];if(r){// for(int mm=2;mm<=M;mm++) if(mm != m) nx[mm][1] += dp[m][r];nx[m][1] -= dp[m][r];off += dp[m][r];}}for(int m=2;m<=M;m++) nx[m][1] += off;}rep1(m,100) rep(r,m){dp[m][r] = nx[m][r], nx[m][r] = 0;if(r) f[i] += dp[m][r];}}return f;};V<mint> f = brute(M*(M+1));show(f);auto c = berlekamp_massey(f);reverse(all(c));show(c);cout << linearRecurrenceAt(f,c,N-1) << endl;show(brute(N)[N-1]);}