結果
問題 | No.981 一般冪乗根 |
ユーザー | eQe |
提出日時 | 2024-11-01 13:32:37 |
言語 | C++23 (gcc 12.3.0 + boost 1.83.0) |
結果 |
RE
|
実行時間 | - |
コード長 | 8,676 bytes |
コンパイル時間 | 7,296 ms |
コンパイル使用メモリ | 337,556 KB |
実行使用メモリ | 6,824 KB |
最終ジャッジ日時 | 2024-11-01 13:33:34 |
合計ジャッジ時間 | 53,971 ms |
ジャッジサーバーID (参考情報) |
judge3 / judge1 |
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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 | RE | - |
testcase_01 | RE | - |
testcase_02 | RE | - |
testcase_03 | RE | - |
testcase_04 | RE | - |
testcase_05 | RE | - |
testcase_06 | RE | - |
testcase_07 | RE | - |
testcase_08 | RE | - |
testcase_09 | RE | - |
testcase_10 | RE | - |
testcase_11 | RE | - |
testcase_12 | RE | - |
testcase_13 | RE | - |
testcase_14 | RE | - |
testcase_15 | RE | - |
testcase_16 | RE | - |
testcase_17 | RE | - |
testcase_18 | RE | - |
testcase_19 | RE | - |
testcase_20 | RE | - |
testcase_21 | RE | - |
testcase_22 | RE | - |
testcase_23 | RE | - |
testcase_24 | RE | - |
testcase_25 | AC | 4 ms
6,820 KB |
testcase_26 | AC | 4 ms
6,820 KB |
testcase_27 | RE | - |
testcase_28 | RE | - |
evil_60bit1.txt | RE | - |
evil_60bit2.txt | RE | - |
evil_60bit3.txt | RE | - |
evil_hack | RE | - |
evil_hard_random | RE | - |
evil_hard_safeprime.txt | RE | - |
evil_hard_tonelli0 | RE | - |
evil_hard_tonelli1 | RE | - |
evil_hard_tonelli2 | RE | - |
evil_hard_tonelli3 | RE | - |
evil_sefeprime1.txt | RE | - |
evil_sefeprime2.txt | RE | - |
evil_sefeprime3.txt | RE | - |
evil_tonelli1.txt | RE | - |
evil_tonelli2.txt | RE | - |
ソースコード
#include<bits/stdc++.h> #include<atcoder/all> namespace my{ using namespace std; using ml=atcoder::modint; auto&operator>>(istream&i,ml&x){int t;i>>t;x=t;return i;} auto&operator<<(ostream&o,const ml&x){return o<<(int)x.val();} #define eb emplace_back #define LL(...) ll __VA_ARGS__;lin(__VA_ARGS__) #define FO(n) for(ll ij=n;ij--;) #define FOR(i,...) for(auto[i,i##stop,i##step]=range(0,__VA_ARGS__);i<i##stop;i+=i##step) #define fo(i,...) FO##__VA_OPT__(R)(i __VA_OPT__(,__VA_ARGS__)) #define of(i,...) for(auto[i,i##stop,i##step]=range(1,__VA_ARGS__);i>=i##stop;i-=i##step) #define fe(a,i,...) for(auto&&__VA_OPT__([)i __VA_OPT__(,__VA_ARGS__]):a) #define single_testcase void solve();}int main(){my::io();my::solve();}namespace my{ void io(){cin.tie(nullptr)->sync_with_stdio(0);cout<<fixed<<setprecision(15);} using ll=long long; using ull=unsigned long long; using ulll=__uint128_t; using lll=__int128_t; istream&operator>>(istream&i,ulll&x){ull t;i>>t;x=t;return i;} ostream&operator<<(ostream&o,const ulll&x){return(x<10?o:o<<x/10)<<ll(x%10);} istream&operator>>(istream&i,lll&x){ll t;i>>t;x=t;return i;} ostream&operator<<(ostream&o,const lll&x){return o<<string(x<0,'-')<<ulll(x>0?x:-x);} auto range(bool s,auto...a){array<ll,3>r{0,0,1};ll I=0;((r[I++]=a),...);if(!s&&I==1)swap(r[0],r[1]);r[0]-=s;return r;} constexpr char nl=10; constexpr char sp=32; lll pw(lll x,ll n){assert(n>=0);lll r=1;while(n)n&1?r*=x:r,x*=x,n>>=1;return r;} template<class A,class B>struct pair{ A a;B b; pair()=default; pair(A a,B b):a(a),b(b){} pair(const std::pair<A,B>&p):a(p.first),b(p.second){} auto operator<=>(const pair&)const=default; friend ostream&operator<<(ostream&o,const pair&p){return o<<p.a<<sp<<p.b;} }; template<class F=less<>>auto&sort(auto&a,const F&f={}){ranges::sort(a,f);return a;} template<class T,class U>ostream&operator<<(ostream&o,const std::pair<T,U>&p){return o<<p.first<<sp<<p.second;} template<class T,size_t n>ostream&operator<<(ostream&o,const array<T,n>&a){fo(i,n)o<<a[i]<<string(i!=n-1,sp);return o;} template<class T,class U>ostream&operator<<(ostream&o,const unordered_map<T,U>&m){fe(m,e)o<<e.first<<sp<<e.second<<nl;return o;} template<class V>concept vectorial=is_base_of_v<vector<typename V::value_type>,V>; template<class V>istream&operator>>(istream&i,vector<V>&v){fe(v,e)i>>e;return i;} template<class V>ostream&operator<<(ostream&o,const vector<V>&v){fe(v,e)o<<e<<string(&e!=&v.back(),vectorial<V>?nl:sp);return o;} template<class V>struct vec:vector<V>{ using vector<V>::vector; vec(const vector<V>&v){vector<V>::operator=(v);} vec&operator^=(const vec&u){this->insert(this->end(),u.begin(),u.end());return*this;} vec operator^(const vec&u)const{return vec{*this}^=u;} vec&operator++(){fe(*this,e)++e;return*this;} vec&operator--(){fe(*this,e)--e;return*this;} }; void lin(auto&...a){(cin>>...>>a);} template<char c=sp>void pp(const auto&...a){ll n=sizeof...(a);((cout<<a<<string(--n>0,c)),...);cout<<nl;} template<class T,class U=T>auto rle(const vec<T>&a){vec<pair<T,U>>r;fe(a,e)r.size()&&e==r.back().a?++r.back().b:r.eb(e,1).b;return r;} template<class T,class U=T>auto rce(vec<T>a){return rle<T,U>(sort(a));} uint64_t kth_root_floor(uint64_t a,ll k){ if (k==1)return a; auto is_within=[&](uint32_t x){uint64_t t=1;fo(k)if(__builtin_mul_overflow(t,x,&t))return false;return t<=a;}; uint64_t r=0; of(i,sizeof(uint32_t)*CHAR_BIT)if(is_within(r|(1u<<i)))r|=1u<<i; return r; } auto sqrt_floor(auto x){return kth_root_floor(x,2);} ll rand(auto...a){array<ll,2>v{0,0};ll I=0;((v[I++]=a),...);auto[l,r]=v;if(I==1)swap(l,r);static ll t=495;t^=t<<7,t^=t>>9;return l<r?(t%(r-l)+(t%(r-l)<0?r-l:0))+l:t;} struct montgomery64{ using i64=__int64_t; using u64=__uint64_t; using u128=__uint128_t; static inline u64 N=998244353; static inline u64 N_inv; static inline u64 R2; static void set_mod(u64 N){ assert(N<(1ULL<<63)); assert(N&1); montgomery64::N=N; R2=-u128(N)%N; N_inv=N; fo(5)N_inv*=2-N*N_inv; assert(N*N_inv==1); } static u64 mod(){ return N; } u64 a; montgomery64(const i64&a=0):a(reduce((u128)(a%(i64)N+N)*R2)){} static u64 reduce(const u128&T){ u128 r=(T+u128(u64(T)*-N_inv)*N)>>64; return r>=N?r-N:r; } auto&operator+=(const montgomery64&b){if((a+=b.a)>=N)a-=N;return*this;} auto&operator-=(const montgomery64&b){if(i64(a-=b.a)<0)a+=N;return*this;} auto&operator*=(const montgomery64&b){a=reduce(u128(a)*b.a);return*this;} auto&operator/=(const montgomery64&b){*this*=b.inv();return*this;} auto operator+(const montgomery64&b)const{return montgomery64(*this)+=b;} auto operator-(const montgomery64&b)const{return montgomery64(*this)-=b;} auto operator*(const montgomery64&b)const{return montgomery64(*this)*=b;} auto operator/(const montgomery64&b)const{return montgomery64(*this)/=b;} bool operator==(const montgomery64&b)const{return a==b.a;} auto operator-()const{return montgomery64()-montgomery64(*this);} montgomery64 pow(u128 n)const{ montgomery64 r{1},x{*this}; while(n){ if(n&1)r*=x; x*=x; n>>=1; } return r; } montgomery64 inv()const{u64 a=val(),b=N,u=1,v=0;while(b)swap(u-=a/b*v,v),swap(a-=a/b*b,b);return u;} u64 val()const{return reduce(a);} friend istream&operator>>(istream&i,montgomery64&b){ll t;i>>t;b=t;return i;} friend ostream&operator<<(ostream&o,const montgomery64&b){return o<<b.val();} }; template<class modular>bool miller_rabin(ll n,vec<ll>as){ ll d=n-1; while(~d&1)d>>=1; if((ll)modular::mod()!=n)modular::set_mod(n); modular one=1,minus_one=n-1; fe(as,a){ if(a%n==0)continue; ll t=d; modular y=modular(a).pow(t); while(t!=n-1&&y!=one&&y!=minus_one)y*=y,t<<=1; if(y!=minus_one&&~t&1)return 0; } return 1; } bool is_prime(ll n){ if(~n&1)return n==2; if(n<=1)return 0; if(n<4759123141LL)return miller_rabin<montgomery64>(n,{2,7,61}); return miller_rabin<montgomery64>(n,{2,325,9375,28178,450775,9780504,1795265022}); } template<class modular>ll pollard_rho(ll n){ if(~n&1)return 2; if(is_prime(n))return n; if((ll)modular::mod()!=n)modular::set_mod(n); modular R,one=1; auto f=[&](const modular&x){return x*x+R;}; while(1){ modular x,y,ys,q=one; R=rand(2,n),y=rand(2,n); ll g=1; constexpr ll m=128; for(ll r=1;g==1;r<<=1){ x=y; fo(r)y=f(y); for(ll k=0;g==1&&k<r;k+=m){ ys=y; for(ll i=0;i<m&&i<r-k;++i)q*=x-(y=f(y)); g=std::gcd(q.val(),n); } } if(g==n)do g=std::gcd((x-(ys=f(ys))).val(),n);while(g==1); if(g!=n)return g; } } auto factorize(ll n){ assert(n>0); auto f=[](auto&f,ll m){ if(m==1)return vec<ll>{}; ll d=pollard_rho<montgomery64>(m); return d==m?vec<ll>{d}:f(f,d)^f(f,m/d); }; return rce(f(f,n)); } template<class T,class U>common_type_t<T,U>gcd(T a,U b){return b?gcd(b,a%b):a>0?a:-a;} template<class...A>auto gcd(const A&...a){common_type_t<A...>r=0;((r=gcd(r,a)),...);return r;} auto mod(auto a,auto m){return(a%=m)<0?a+m:a;} auto inv_mod(auto x,auto m){assert(gcd(x,m)==1);decltype(x)a=mod(x,m),b=m,u=1,v=0;while(b)swap(u-=a/b*v,v),swap(a-=a/b*b,b);return mod(u,m);} ll kth_root_mod_prime(ll a,ll k,ll P){ if(k==0)return(a==1?1:-1); if(a==0)return 0; if(P==2)return a; k=mod(k,P-1); using ml=atcoder::modint; ml::set_mod(P); ll g=gcd(k,P-1); if(ml(a).pow((P-1)/g)!=1)return-1; ll c=inv_mod(k/g,(P-1)/g); a=ml(a).pow(c).val(); k=(lll)k*c%(P-1); if(k==0)return 1; auto pe_root=[&](ml c,ll p,ll e){ ll t=0; ll pt=1; ll s=P-1; while(s%p==0)++t,s/=p; ll pt1=pt/p; ml v=1; while(v.pow((P-1)/p)==1)v+=1; ll pe=pw(p,e); ll u=inv_mod(-s,pe); ml z=c.pow(((lll)s*u+1)/pe); ml c_inv=c.inv(); while(1){ ml zpe_c=z.pow(pe)*c_inv; ll t_dash=0; while(zpe_c.pow(pw(p,t_dash))!=1)++t_dash; if(t_dash==0)break; ll E=t-t_dash; ml vspE=v.pow((lll)s*pw(p,E-e)); ml A=v.pow((lll)s*pt1),A_inv=A.inv(); ml B=zpe_c.inv().pow(pw(p,t_dash-1)); ll R=sqrt_floor(p)+1; unordered_map<ll,int>dict; ll k=-1; ml A_inv_R=A_inv.pow(R); ml A_inv_pow=1; fo(i,R){ dict[(B*A_inv_pow).val()]=i; A_inv_pow*=A_inv_R; } ml A_pow=1; fo(j,R){ if(ll key=A_pow.val();dict.contains(key)){ k=R*dict[key]+j; break; } A_pow*=A; } z*=vspE.pow(k); } return z.val(); }; fe(factorize(k),p,e)a=pe_root(a,p,e); return a; } single_testcase void solve(){ LL(T); fo(T){ LL(P,k,a); pp(kth_root_mod_prime(a,k,P)); } }}