結果

問題 No.181 A↑↑N mod M
コンテスト
ユーザー Nachia
提出日時 2023-01-11 16:29:00
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 4 ms / 5,000 ms
コード長 5,250 bytes
コンパイル時間 1,075 ms
コンパイル使用メモリ 83,572 KB
最終ジャッジ日時 2025-02-10 01:39:22
ジャッジサーバーID
（参考情報） 		judge5 / judge3
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ファイルパターン 結果
sample AC * 6
other AC * 37
権限があれば一括ダウンロードができます
コンパイルメッセージ
Main.cpp: In function ‘int main()’:
Main.cpp:5:30: warning: ignoring return value of ‘int scanf(const char*, ...)’ declared with attribute ‘warn_unused_result’ [-Wunused-result]

ソースコード

diff #
raw source code 

#line 2 "nachia\\math-modulo\\tetration-mod.hpp"

#line 2 "nachia\\math\\isprime.hpp"
#include <initializer_list>

namespace nachia{

bool IsPrime(unsigned long long x) noexcept {
    if(x <= 1) return false;
    if(x % 2 == 0) return x == 2;
    using u64 = unsigned long long;
    using u128 = __uint128_t;
    u64 d = x-1;
    int s = 0;
    int q = 63;
    while(!(d&1)){ d >>= 1; s++; }
    while(!(d >> q)) q--;
    u64 r = x; for(int t=0; t<6; t++) r*=2-r*x;
    u128 n2 = -(u128)x % x;
    auto red = [=](u128 t) noexcept -> u64 {
        t = (t + (u128)((u64)t*-r)*x) >> 64;
        return (t >= x) ? t-x : t;
    };
    u64 one = red(n2);
    for(u64 base : { 2, 325, 9375, 28178, 450775, 9780504, 1795265022 }){
        if(base%x==0) continue;
        u64 a = base = red(base%x*n2);
        for(int e=q-1; e>=0; e--){ a = red((u128)a*a); if((d>>e)&1) a = red((u128)a*base); }
        if(a == one) continue;
        for(int t=1; t<s&&a!=x-one; t++) a = red((u128)a*a);
        if(a != x-one) return false;
    }
    return true;
}

} // namespace nachia
#line 2 "nachia\\misc\\bit-operations.hpp"
#include <vector>
#include <algorithm>

namespace nachia{

int Popcount(unsigned long long c) noexcept {
#ifdef __GNUC__
    return __builtin_popcountll(c);
#else
    c = (c & (~0ull/3)) + ((c >> 1) & (~0ull/3));
    c = (c & (~0ull/5)) + ((c >> 2) & (~0ull/5));
    c = (c & (~0ull/17)) + ((c >> 4) & (~0ull/17));
    c = (c * (~0ull/257)) >> 56;
    return c;
#endif
}

// please ensure x != 0
int MsbIndex(unsigned long long x) noexcept {
#ifdef __GNUC__
    return 63 - __builtin_clzll(x);
#else
    int res = 0;
    for(int d=32; d>0; d>>=1) if(x >> d){ res |= d; x >>= d; }
    return res;
#endif
}

// please ensure x != 0
int LsbIndex(unsigned long long x) noexcept {
#ifdef __GNUC__
    return __builtin_ctzll(x);
#else
    return MsbIndex(x & -x);
#endif
}

}

#line 5 "nachia\\math\\factorize.hpp"
#include <utility>

namespace nachia{

std::vector<std::pair<unsigned long long, int>> Factorize(unsigned long long x){
    if(x == 1) return {};
    if(IsPrime(x)) return {{x,1}};
    using u64 = unsigned long long;
    using u128 = __uint128_t;
    u64 X = x;
    std::vector<u64> p;
    for(u64 i=2; i<100; i+=1+i%2) if(x%i==0){ p.push_back(i); while(x%i==0) x/=i; }
    u64 r=1; u128 n2=1;
    auto updX = [&](){
        r = x; for(int t=0; t<6; t++) r*=2-r*x;
        n2 = -(u128)x % x;
    };
    auto red = [&](u128 t) noexcept -> u64 {
        t = (t + (u128)((u64)t*-r)*x) >> 64;
        return (t >= x) ? t-x : t;
    };
    auto mult = [&](u64 a, u64 b) noexcept { return red((u128)red((u128)a*n2)*b); };
    auto f = [&](u64 a) noexcept -> u64 { return red((u128)a*a+1); };
    auto gcd = [](u64 a, u64 b) noexcept {
        if(!a || !b) return a|b;
        int q = LsbIndex(a|b);
        b >>= LsbIndex(b);
        a >>= LsbIndex(a);
        while(a!=b){
            if(a<b){ b-=a; b>>=LsbIndex(b); }
            else{ a-=b; a>>=LsbIndex(a); }
        }
        return a<<q;
    };
    static u64 v = 7001;
    p.push_back(x);
    for(int pi=p.size()-1; pi<(int)p.size(); pi++) while(p[pi] != 1 && !IsPrime(p[pi])){
        x = p[pi]; updX();
        while(p[pi] == x){
            v^=v<<13; v^=v>>7; v^=v<<17; // Xorshift https://www.jstatsoft.org/article/download/v008i14/916
            u64 a = v%x, b = f(a);
            u64 buf = a, sz = 1, nx = 10;
            while(true){
                while(nx != sz && a != b){
                    buf = mult(buf, a<=b?b-a:a-b); sz++;
                    a = f(a); b = f(f(b));
                }
                u64 g = gcd(buf, x);
                if(g != 1){
                    while(p[pi] % g == 0) p[pi] /= g;
                    p.push_back(g);
                    break;
                }
                if(a == b) break;
                nx = sz * 3 / 2;
            }
        }
    }
    std::vector<std::pair<u64, int>> res;
    for(u64 q : p) if(q != 1){
        int e=0; while(X%q == 0){ e++; X/=q; }
        if(e) res.push_back({ q, e });
    }
    return res;
}

unsigned long long Totient(unsigned long long x){
    auto F = Factorize(x);
    for(auto f : F) x -= x / f.first;
    return x;
}

} // namespace nachia
#line 4 "nachia\\math-modulo\\tetration-mod.hpp"
#include <iostream>
using namespace std;

namespace nachia{

// A ^^ B mod M
unsigned int TetrationMod(unsigned int A, unsigned int B, unsigned int M){
    if(A == 0) return (1-B%2)%M;
    if(A == 1 || B == 0) return 1%M;
    using u64 = unsigned long long;
    auto mod2 = [&](u64 a, u64 m) noexcept { return a>=m ? a%m+m : a; };
    auto mult = [&](u64 a, u64 b, u64 m) noexcept { return mod2(a*b,m); };
    auto powm = [&](u64 a, u64 i, u64 m) noexcept { u64 r = 1; while(i){ if(i&1){ r=mult(r,a,m); } a=mult(a,a,m); i>>=1; } return r; };
    std::vector<u64> M2 = {M};
    while(M2.size() < B && M2.back() != 1) M2.push_back(Totient(M2.back()));
    B = M2.size();
    u64 res = 1;
    for(int i=B-1; i>=0; i--) res = powm(mod2(A, M2[i]), res, M2[i]);
    return res % M;
}

} // namespace nachia
#line 2 "Main.cpp"
#include <cstdio>

int main(){
    unsigned int A,B,M; scanf("%u%u%u", &A, &B, &M);
    unsigned int ans = nachia::TetrationMod(A, B, M);
    printf("%u\n", ans);
	return 0;
}
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