結果
問題 | No.1025 Modular Equation |
ユーザー |
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提出日時 | 2020-04-11 01:10:19 |
言語 | C++14 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 818 ms / 5,000 ms |
コード長 | 7,718 bytes |
コンパイル時間 | 1,910 ms |
コンパイル使用メモリ | 175,568 KB |
実行使用メモリ | 29,440 KB |
最終ジャッジ日時 | 2024-09-16 05:32:17 |
合計ジャッジ時間 | 21,410 ms |
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 * 32 |
ソースコード
#include <bits/stdc++.h>using namespace std;using ll=long long;#define int ll#define rng(i,a,b) for(int i=int(a);i<int(b);i++)#define rep(i,b) rng(i,0,b)#define gnr(i,a,b) for(int i=int(b)-1;i>=int(a);i--)#define per(i,b) gnr(i,0,b)#define pb push_back#define eb emplace_back#define a first#define b second#define bg begin()#define ed end()#define all(x) x.bg,x.ed#define si(x) int(x.size())#ifdef LOCAL#define dmp(x) cerr<<__LINE__<<" "<<#x<<" "<<x<<endl#else#define dmp(x) void(0)#endiftemplate<class t,class u> void chmax(t&a,u b){if(a<b)a=b;}template<class t,class u> void chmin(t&a,u b){if(b<a)a=b;}template<class t> using vc=vector<t>;template<class t> using vvc=vc<vc<t>>;using pi=pair<int,int>;using vi=vc<int>;template<class t,class u>ostream& operator<<(ostream& os,const pair<t,u>& p){return os<<"{"<<p.a<<","<<p.b<<"}";}template<class t> ostream& operator<<(ostream& os,const vc<t>& v){os<<"{";for(auto e:v)os<<e<<",";return os<<"}";}#define mp make_pair#define mt make_tuple#define one(x) memset(x,-1,sizeof(x))#define zero(x) memset(x,0,sizeof(x))#ifdef LOCALvoid 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 dmp2(...) dmpr(cerr,__LINE__,##__VA_ARGS__)#else#define dmp2(...) void(0)#endifusing uint=unsigned;using ull=unsigned long long;template<class t,size_t n>ostream& operator<<(ostream&os,const array<t,n>&a){return os<<vc<t>(all(a));}template<int i,class T>void print_tuple(ostream&,const T&){}template<int i,class T,class H,class ...Args>void print_tuple(ostream&os,const T&t){if(i)os<<",";os<<get<i>(t);print_tuple<i+1,T,Args...>(os,t);}template<class ...Args>ostream& operator<<(ostream&os,const tuple<Args...>&t){os<<"{";print_tuple<0,tuple<Args...>,Args...>(os,t);return os<<"}";}template<class t>void print(t x,int suc=1){cout<<x;if(suc==1)cout<<"\n";if(suc==2)cout<<" ";}ll read(){ll i;cin>>i;return i;}vi readvi(int n,int off=0){vi v(n);rep(i,n)v[i]=read()+off;return v;}template<class T>void print(const vector<T>&v,int suc=1){rep(i,v.size())print(v[i],i==int(v.size())-1?suc:2);}string readString(){string s;cin>>s;return s;}template<class T>T sq(const T& t){return t*t;}//#define CAPITALvoid yes(bool ex=true){#ifdef CAPITALcout<<"YES"<<"\n";#elsecout<<"Yes"<<"\n";#endifif(ex)exit(0);}void no(bool ex=true){#ifdef CAPITALcout<<"NO"<<"\n";#elsecout<<"No"<<"\n";#endifif(ex)exit(0);}void possible(bool ex=true){#ifdef CAPITALcout<<"POSSIBLE"<<"\n";#elsecout<<"Possible"<<"\n";#endifif(ex)exit(0);}void impossible(bool ex=true){#ifdef CAPITALcout<<"IMPOSSIBLE"<<"\n";#elsecout<<"Impossible"<<"\n";#endifif(ex)exit(0);}constexpr ll ten(int n){return n==0?1:ten(n-1)*10;}const ll infLL=LLONG_MAX/3;#ifdef intconst int inf=infLL;#elseconst int inf=INT_MAX/2-100;#endifint topbit(signed t){return t==0?-1:31-__builtin_clz(t);}int topbit(ll t){return t==0?-1:63-__builtin_clzll(t);}int botbit(signed a){return a==0?32:__builtin_ctz(a);}int botbit(ll a){return a==0?64:__builtin_ctzll(a);}int popcount(signed t){return __builtin_popcount(t);}int popcount(ll t){return __builtin_popcountll(t);}bool ispow2(int i){return i&&(i&-i)==i;}ll mask(int i){return (ll(1)<<i)-1;}bool inc(int a,int b,int c){return a<=b&&b<=c;}template<class t> void mkuni(vc<t>&v){sort(all(v));v.erase(unique(all(v)),v.ed);}ll rand_int(ll l, ll r) { //[l, r]#ifdef LOCALstatic mt19937_64 gen;#elsestatic mt19937_64 gen(chrono::steady_clock::now().time_since_epoch().count());#endifreturn uniform_int_distribution<ll>(l, r)(gen);}template<class t>void myshuffle(vc<t>&a){rep(i,si(a))swap(a[i],a[rand_int(0,i)]);}template<class t>int lwb(const vc<t>&v,const t&a){return lower_bound(all(v),a)-v.bg;}using uint=unsigned;using ull=unsigned long long;struct modinfo{uint mod,root;};template<modinfo const&ref>struct modular{static constexpr uint const &mod=ref.mod;static modular root(){return modular(ref.root);}uint v;//modular(initializer_list<uint>ls):v(*ls.bg){}modular(ll vv=0){s(vv%mod+mod);}modular& s(uint vv){v=vv<mod?vv:vv-mod;return *this;}modular operator-()const{return modular()-*this;}modular& operator+=(const modular&rhs){return s(v+rhs.v);}modular&operator-=(const modular&rhs){return s(v+mod-rhs.v);}modular&operator*=(const modular&rhs){v=ull(v)*rhs.v%mod;return *this;}modular&operator/=(const modular&rhs){return *this*=rhs.inv();}modular operator+(const modular&rhs)const{return modular(*this)+=rhs;}modular operator-(const modular&rhs)const{return modular(*this)-=rhs;}modular operator*(const modular&rhs)const{return modular(*this)*=rhs;}modular operator/(const modular&rhs)const{return modular(*this)/=rhs;}modular pow(int n)const{modular res(1),x(*this);while(n){if(n&1)res*=x;x*=x;n>>=1;}return res;}modular inv()const{return pow(mod-2);}/*modular inv()const{int x,y;int g=extgcd(v,mod,x,y);assert(g==1);if(x<0)x+=mod;return modular(x);}*/friend modular operator+(int x,const modular&y){return modular(x)+y;}friend modular operator-(int x,const modular&y){return modular(x)-y;}friend modular operator*(int x,const modular&y){return modular(x)*y;}friend modular operator/(int x,const modular&y){return modular(x)/y;}friend ostream& operator<<(ostream&os,const modular&m){return os<<m.v;}friend istream& operator>>(istream&is,modular&m){ll x;is>>x;m=modular(x);return is;}bool operator<(const modular&r)const{return v<r.v;}bool operator==(const modular&r)const{return v==r.v;}bool operator!=(const modular&r)const{return v!=r.v;}explicit operator bool()const{return v;}};//extern constexpr modinfo base{998244353,3};extern constexpr modinfo base{1000000007,0};//modinfo base{1,0};using mint=modular<base>;const int vmax=(1<<21)+10;mint fact[vmax],finv[vmax],invs[vmax];void initfact(){fact[0]=1;rng(i,1,vmax){fact[i]=fact[i-1]*i;}finv[vmax-1]=fact[vmax-1].inv();for(int i=vmax-2;i>=0;i--){finv[i]=finv[i+1]*(i+1);}for(int i=vmax-1;i>=1;i--){invs[i]=finv[i]*fact[i-1];}}mint choose(int n,int k){return fact[n]*finv[n-k]*finv[k];}mint binom(int a,int b){return fact[a+b]*finv[a]*finv[b];}mint catalan(int n){return binom(n,n)-(n-1>=0?binom(n-1,n+1):0);}int gcd(int a,int b){return b?gcd(b,a%b):a;}template<class t>t pow_mod(t x,t n,t m){t r=1;while(n){if(n&1)r=(r*x)%m;x=(x*x)%m;n>>=1;}return r;}//assume p is a primebool is_primitiveroot(int r,int p){if(!r)return false;int x=p-1;for(int i=2;i*i<=x;i++){if(x%i==0){int w=pow_mod<int>(r,(p-1)/i,p);if(w==1)return false;while(x%i==0)x/=i;}}if(x>1&&pow_mod<int>(r,(p-1)/x,p)==1)return false;return true;}//assume p is a primeint get_primitiveroot(int p){rng(w,1,p)if(is_primitiveroot(w,p))return w;assert(false);}signed main(){cin.tie(0);ios::sync_with_stdio(0);cout<<fixed<<setprecision(20);int p,n,k,b;cin>>p>>n>>k>>b;k=gcd(k,p-1);int w=get_primitiveroot(p);vi val(p-1);{int x=1;rep(i,p-1){val[i]=x;x=x*w%p;}}vc<mint> dp(p),tmp(p);dp[0]=1;rep(_,n){int a;cin>>a;if(a==0){rep(i,p)dp[i]*=p;}else{rep(i,p)tmp[(i+a)%p]=dp[i];rep(i,k){mint sum;for(int j=i;j<p-1;j+=k)sum+=tmp[val[j]];sum*=k;for(int j=i;j<p-1;j+=k)dp[val[j]]+=sum;}dp[0]+=tmp[0]*(p-1);}}cout<<dp[b]<<endl;}