結果
| 問題 | No.1025 Modular Equation |
| ユーザー |
 beet
|
| 提出日時 | 2020-04-10 23:16:36 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
WA
|
| 実行時間 | - |
| コード長 | 7,474 bytes |
| コンパイル時間 | 2,603 ms |
| コンパイル使用メモリ | 215,596 KB |
| 最終ジャッジ日時 | 2025-01-09 16:51:16 |
|
ジャッジサーバーID （参考情報） |
judge2 / judge2 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 WA * 1 |
| other | AC * 4 WA * 28 |
ソースコード
#include <bits/stdc++.h>using namespace std;template<typename T1,typename T2> inline void chmin(T1 &a,T2 b){if(a>b) a=b;}template<typename T1,typename T2> inline void chmax(T1 &a,T2 b){if(a<b) a=b;}using Int = long long;const char newl = '\n';template<typename T,T MOD = 1000000007>struct Mint{static constexpr T mod = MOD;T v;Mint():v(0){}Mint(signed v):v(v){}Mint(long long t){v=t%MOD;if(v<0) v+=MOD;}Mint pow(long long k){Mint res(1),tmp(v);while(k){if(k&1) res*=tmp;tmp*=tmp;k>>=1;}return res;}static Mint add_identity(){return Mint(0);}static Mint mul_identity(){return Mint(1);}Mint inv(){return pow(MOD-2);}Mint& operator+=(Mint a){v+=a.v;if(v>=MOD)v-=MOD;return *this;}Mint& operator-=(Mint a){v+=MOD-a.v;if(v>=MOD)v-=MOD;return *this;}Mint& operator*=(Mint a){v=1LL*v*a.v%MOD;return *this;}Mint& operator/=(Mint a){return (*this)*=a.inv();}Mint operator+(Mint a) const{return Mint(v)+=a;}Mint operator-(Mint a) const{return Mint(v)-=a;}Mint operator*(Mint a) const{return Mint(v)*=a;}Mint operator/(Mint a) const{return Mint(v)/=a;}Mint operator-() const{return v?Mint(MOD-v):Mint(v);}bool operator==(const Mint a)const{return v==a.v;}bool operator!=(const Mint a)const{return v!=a.v;}bool operator <(const Mint a)const{return v <a.v;}static Mint comb(long long n,int k){Mint num(1),dom(1);for(int i=0;i<k;i++){num*=Mint(n-i);dom*=Mint(i+1);}return num/dom;}};template<typename T,T MOD> constexpr T Mint<T, MOD>::mod;template<typename T,T MOD>ostream& operator<<(ostream &os,Mint<T, MOD> m){os<<m.v;return os;}namespace FFT{using dbl = double;struct num{dbl x,y;num(){x=y=0;}num(dbl x,dbl y):x(x),y(y){}};inline num operator+(num a,num b){return num(a.x+b.x,a.y+b.y);}inline num operator-(num a,num b){return num(a.x-b.x,a.y-b.y);}inline num operator*(num a,num b){return num(a.x*b.x-a.y*b.y,a.x*b.y+a.y*b.x);}inline num conj(num a){return num(a.x,-a.y);}int base=1;vector<num> rts={{0,0},{1,0}};vector<int> rev={0,1};const dbl PI=asinl(1)*2;void ensure_base(int nbase){if(nbase<=base) return;rev.resize(1<<nbase);for(int i=0;i<(1<<nbase);i++)rev[i]=(rev[i>>1]>>1)+((i&1)<<(nbase-1));rts.resize(1<<nbase);while(base<nbase){dbl angle=2*PI/(1<<(base+1));for(int i=1<<(base-1);i<(1<<base);i++){rts[i<<1]=rts[i];dbl angle_i=angle*(2*i+1-(1<<base));rts[(i<<1)+1]=num(cos(angle_i),sin(angle_i));}base++;}}void fft(vector<num> &as){int n=as.size();assert((n&(n-1))==0);int zeros=__builtin_ctz(n);ensure_base(zeros);int shift=base-zeros;for(int i=0;i<n;i++)if(i<(rev[i]>>shift))swap(as[i],as[rev[i]>>shift]);for(int k=1;k<n;k<<=1){for(int i=0;i<n;i+=2*k){for(int j=0;j<k;j++){num z=as[i+j+k]*rts[j+k];as[i+j+k]=as[i+j]-z;as[i+j]=as[i+j]+z;}}}}template<typename T>vector<long long> multiply(vector<T> &as,vector<T> &bs){int need=as.size()+bs.size()-1;int nbase=0;while((1<<nbase)<need) nbase++;ensure_base(nbase);int sz=1<<nbase;vector<num> fa(sz);for(int i=0;i<sz;i++){T x=(i<(int)as.size()?as[i]:0);T y=(i<(int)bs.size()?bs[i]:0);fa[i]=num(x,y);}fft(fa);num r(0,-0.25/sz);for(int i=0;i<=(sz>>1);i++){int j=(sz-i)&(sz-1);num z=(fa[j]*fa[j]-conj(fa[i]*fa[i]))*r;if(i!=j)fa[j]=(fa[i]*fa[i]-conj(fa[j]*fa[j]))*r;fa[i]=z;}fft(fa);vector<long long> res(need);for(int i=0;i<need;i++)res[i]=round(fa[i].x);return res;}};template<typename T>struct ArbitraryMod{using dbl=FFT::dbl;using num=FFT::num;vector<T> multiply(vector<T> as,vector<T> bs){int need=as.size()+bs.size()-1;int sz=1;while(sz<need) sz<<=1;vector<num> fa(sz),fb(sz);for(int i=0;i<(int)as.size();i++)fa[i]=num(as[i].v&((1<<15)-1),as[i].v>>15);for(int i=0;i<(int)bs.size();i++)fb[i]=num(bs[i].v&((1<<15)-1),bs[i].v>>15);fft(fa);fft(fb);dbl ratio=0.25/sz;num r2(0,-1),r3(ratio,0),r4(0,-ratio),r5(0,1);for(int i=0;i<=(sz>>1);i++){int j=(sz-i)&(sz-1);num a1=(fa[i]+conj(fa[j]));num a2=(fa[i]-conj(fa[j]))*r2;num b1=(fb[i]+conj(fb[j]))*r3;num b2=(fb[i]-conj(fb[j]))*r4;if(i!=j){num c1=(fa[j]+conj(fa[i]));num c2=(fa[j]-conj(fa[i]))*r2;num d1=(fb[j]+conj(fb[i]))*r3;num d2=(fb[j]-conj(fb[i]))*r4;fa[i]=c1*d1+c2*d2*r5;fb[i]=c1*d2+c2*d1;}fa[j]=a1*b1+a2*b2*r5;fb[j]=a1*b2+a2*b1;}fft(fa);fft(fb);vector<T> cs(need);using ll = long long;for(int i=0;i<need;i++){ll aa=T(llround(fa[i].x)).v;ll bb=T(llround(fb[i].x)).v;ll cc=T(llround(fa[i].y)).v;cs[i]=T(aa+(bb<<15)+(cc<<30));}return cs;}};template<typename T>struct Rint{static T mod;static void set_mod(T nmod){mod=nmod;}T v;Rint():v(0){}Rint(signed v):v(v){}Rint(long long t){v=t%mod;if(v<0) v+=mod;}Rint pow(long long k){Rint res(1),tmp(v);while(k){if(k&1) res*=tmp;tmp*=tmp;k>>=1;}return res;}static Rint add_identity(){return Rint(0);}static Rint mul_identity(){return Rint(1);}Rint inv(){return pow(mod-2);}Rint& operator+=(Rint a){v+=a.v;if(v>=mod)v-=mod;return *this;}Rint& operator-=(Rint a){v+=mod-a.v;if(v>=mod)v-=mod;return *this;}Rint& operator*=(Rint a){v=1LL*v*a.v%mod;return *this;}Rint& operator/=(Rint a){return (*this)*=a.inv();}Rint operator+(Rint a) const{return Rint(v)+=a;}Rint operator-(Rint a) const{return Rint(v)-=a;}Rint operator*(Rint a) const{return Rint(v)*=a;}Rint operator/(Rint a) const{return Rint(v)/=a;}Rint operator-() const{return v?Rint(mod-v):Rint(v);}bool operator==(const Rint a)const{return v==a.v;}bool operator!=(const Rint a)const{return v!=a.v;}bool operator <(const Rint a)const{return v <a.v;}};template<typename T> T Rint<T>::mod;template<typename T>ostream& operator<<(ostream &os,Rint<T> m){os<<m.v;return os;}//INSERT ABOVE HEREsigned main(){cin.tie(0);ios::sync_with_stdio(0);int p,n,k,b;cin>>p>>n>>k>>b;vector<int> as(n);for(int i=0;i<n;i++) cin>>as[i];using R = Rint<int>;R::set_mod(p);vector<R> ps(p);for(int i=0;i<p;i++)ps[i]=R(i).pow(k);using M = Mint<int>;ArbitraryMod<M> arb;using Poly = vector<M>;M po{1};map<int, int> cnt,rpr;for(int i=0;i<n;i++){if(as[i]==0) po*=M(p);int o=p;for(int j=0;j<p;j++)chmin(o,(R(as[i])*ps[j]).v);cnt[o]++;rpr[o]=i;}auto mul=[&](Poly &as,Poly &bs){assert((int)as.size()==p);assert((int)bs.size()==p);auto cs=arb.multiply(as,bs);for(int j=p;j<(int)cs.size();j++) cs[j-p]+=cs[j];cs.resize(p);return cs;};Poly dp(p,0);dp[0]=1;for(auto tmp:cnt){int i=rpr[tmp.first];Poly ad(p,0);for(int j=0;j<p;j++)ad[(R(as[i])*ps[j]).v]+=M(1);int x=tmp.second;while(x){if(x&1) dp=mul(dp,ad);x>>=1;if(x) ad=mul(ad,ad);}}cout<<dp[b]*po<<newl;return 0;}