結果

問題 No.2193 メガの下１桁
コンテスト
ユーザー 👑 tatyam
提出日時 2023-01-13 21:53:03
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 2 ms / 2,000 ms
コード長 3,757 bytes
コンパイル時間 7,797 ms
コンパイル使用メモリ 333,104 KB
実行使用メモリ 5,248 KB
最終ジャッジ日時 2024-12-24 17:12:20
合計ジャッジ時間 7,535 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge4
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ファイルパターン 結果
other AC * 40
権限があれば一括ダウンロードができます

ソースコード

diff # 

#include <bits/stdc++.h>
using namespace std;


constexpr uint32_t totient(uint32_t x){
    uint32_t ans = x;
    for(uint32_t i = 2; i * i <= x; i++) if(x % i == 0){
        ans /= i;
        ans *= i - 1;
        do x /= i; while(x % i == 0);
    }
    if(x != 1){
        ans /= x;
        ans *= x - 1;
    }
    return ans;
}
template<uint32_t P> struct Modint{
    static_assert(P < 0x80000000, "P must be smaller than 2^31");
    uint32_t a;
    Modint<totient(P)> b;
private:
    static uint32_t mod(uint64_t x){
        if(x < P * 2) return uint32_t(x);
        return uint32_t(x % P) + P;
    }
    static uint32_t mul(uint32_t a, uint32_t b){
        return mod(uint64_t(a) * b);
    }
    static uint32_t pow(uint32_t a, uint32_t b){
        uint32_t ans = 1;
        while(b){
            if(b & 1) ans = mul(ans, a);
            a = mul(a, a);
            b >>= 1;
        }
        return ans;
    }
public:
    Modint(uint64_t x): a(mod(x)), b(x){}
    Modint(uint32_t a, Modint<totient(P)> b): a(a), b(b){}
    uint32_t val() const {
        if(a < P) return a;
        return a - P;
    }
    Modint& operator*=(const Modint& other){
        a = mul(a, other.a);
        b *= other.b;
        return *this;
    }
    Modint operator*(const Modint& other) const {
        return Modint(*this) *= other;
    }
    Modint& operator+=(const Modint& other){
        a += other.a;
        if(a >= P * 2) a -= P;
        if(a >= P * 2) a -= P;
        b += other.b;
        return *this;
    }
    Modint operator+(const Modint& other) const {
        return Modint(*this) += other;
    }
    Modint pow(const Modint& other) const {
        return {pow(a, other.b.a), b.pow(other.b)};
    };
    bool operator<(const Modint& other) const {
        return tie(a, b) < tie(other.a, other.b);
    }
};
template<> struct Modint<1>{
    uint32_t a;
    Modint(uint64_t x): a(bool(x)){}
    uint32_t val() const {
        return 0;
    }
    Modint& operator*=(const Modint& other){
        a &= other.a;
        return *this;
    }
    Modint operator*(const Modint& other) const {
        return Modint(*this) *= other;
    }
    Modint& operator+=(const Modint& other){
        a |= other.a;
        return *this;
    }
    Modint operator+(const Modint& other) const {
        return Modint(*this) += other;
    }
    Modint pow(const Modint& other) const {
        return {a || !other.a};
    }
    bool operator<(const Modint& other) const {
        return a < other.a;
    }
};
template<int B> int solve(uint64_t M, uint64_t D, uint64_t N) {
    using mint = Modint<B>;
    map<mint, int> press;
    for(int i = 0; i < 1000; i++) press.try_emplace(i, press.size());
    vector table(60, vector<int>(press.size()));
    for(auto& [m, idx] : press) {
        table[0][idx] = press[(m + mint{D}).pow(m)];
    }
    for(int l = 0; l + 1 < 60; l++) for(int i = 0; i < press.size(); i++) table[l + 1][i] = table[l][table[l][i]];
    int ans = press[mint{M}];
    for(int l = 0; l < 60; l++) if(N & 1ULL << l) ans = table[l][ans];
    for(auto& [m, idx] : press) if(ans == idx) return m.a % B;
    abort();
}
int main() {
    uint64_t M, D, N, B;
    cin >> M >> D >> N >> B;
    const int ans = [&]{
        switch (B) {
            case 2: return solve<2>(M, D, N);
            case 3: return solve<3>(M, D, N);
            case 4: return solve<4>(M, D, N);
            case 5: return solve<5>(M, D, N);
            case 6: return solve<6>(M, D, N);
            case 7: return solve<7>(M, D, N);
            case 8: return solve<8>(M, D, N);
            case 9: return solve<9>(M, D, N);
            case 10: return solve<10>(M, D, N);
            default: return solve<11>(M, D, N);
        }
    }();
    cout << hex << uppercase << ans << endl;
}
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