結果

問題 No.3170 [Cherry 7th Tune KY] Even if you could say "See you ..."
ユーザー 👑 Nachia
提出日時 2025-05-30 23:50:55
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 150 ms / 4,000 ms
コード長 5,693 bytes
コンパイル時間 1,024 ms
コンパイル使用メモリ 79,936 KB
実行使用メモリ 6,272 KB
最終ジャッジ日時 2025-06-11 23:06:28
合計ジャッジ時間 4,272 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge2
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 2
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 # 

#ifdef NACHIA
#define _GLIBCXX_DEBUG
#else
#define NDEBUG
#endif
#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
using i64 = long long;
using u64 = unsigned long long;
#define rep(i,n) for(i64 i=0; i<i64(n); i++)
const i64 INF = 1001001001001001001;
template<typename A> void chmin(A& l, const A& r){ if(r < l) l = r; }
template<typename A> void chmax(A& l, const A& r){ if(l < r) l = r; }
using namespace std;

#include <array>
#include <cassert>

#include <utility>
namespace nachia{

// ax + by = gcd(a,b)
// return ( x, - )
std::pair<long long, long long> ExtGcd(long long a, long long b){
    long long x = 1, y = 0;
    while(b){
        long long u = a / b;
        std::swap(a-=b*u, b);
        std::swap(x-=y*u, y);
    }
    return std::make_pair(x, a);
}

} // namespace nachia

namespace nachia{

class DynamicModSupplier{
    using u64 = unsigned long long;
    using Int = unsigned int;
private:
    u64 imod;
    Int mod;
    // atcoder library
    u64 reduce2(u64 z) const noexcept {
        // atcoder library
#ifdef _MSC_VER
        u64 x; _umul128(z, im, &x);
#else
        using u128 = unsigned __int128;
        u64 x = (u64)(((u128)(z)*imod) >> 64);
#endif
        return z - x * mod;
    }
public:
    DynamicModSupplier(unsigned int MOD = 998244353) : mod(MOD) {
        assert(2 <= MOD);
        assert(MOD < (1u << 31));
        imod = (u64)(-1) / mod + 1;
    }
    Int reduce(u64 z) const noexcept {
        Int v = reduce2(z);
        if(mod <= v) v += mod;
        return v;
    }
    Int add(Int a, Int b) const { a += b; if(a >= mod){ a -= mod; } return a; }
    Int sub(Int a, Int b) const { a -= b; if(a >= mod){ a += mod; } return a; }
    Int mul(Int a, Int b) const { return reduce((u64)a * b); }
    Int muladd(Int a, Int b, Int c) const { return reduce((u64)a * b + c); }
    Int inv(Int a) const {
        Int v = ExtGcd(a, mod).first;
        return (v < mod) ? v : (v + mod);
    }
    Int pow(Int a, u64 i) const {
        Int r = a, ans = 1;
        while(i){
            if(i & 1) ans = mul(ans, r);
            i /= 2;
            r = mul(r, r);
        }
        return ans;
    }
    Int getMod() const { return mod; }
};

} // namespace nachia

namespace nachia{

template<unsigned int IDENTIFER, class IDENTIFER2 = void>
class DynamicModint{
    using Int = unsigned int;
    using MyType = DynamicModint;
private:
    static DynamicModSupplier _c;
    Int v;
    template< class Elem >
    static Elem SafeMod(Elem x, Int mod){
        if(x < 0){
            if(0 <= x+mod) return x + mod;
            return mod - ((-(x+mod)-1) % mod + 1);
        }
        return x % mod;
    }
public:
    DynamicModint() : v(0) {}
    DynamicModint(const MyType& r) : v(r.v) {}
    MyType& operator=(const MyType&) = default;
    DynamicModint(long long x){ v = SafeMod(x, _c.getMod()); }
    static MyType raw(Int _v){ MyType res; res.v = _v; return res; }
    static void setMod(DynamicModSupplier sup){ _c = std::move(sup); }
    MyType operator+=(MyType r){ return v = _c.add(v, r.v); }
    MyType operator+(MyType r) const { return raw(_c.add(v, r.v)); }
    MyType operator-=(MyType r){ return v = _c.sub(v, r.v); }
    MyType operator-(MyType r) const { return raw(_c.sub(v, r.v)); }
    MyType operator-() const { return raw(v ? _c.getMod()-v : 0); }
    MyType operator*=(MyType r){ return v = _c.mul(v, r.v); }
    MyType operator*(MyType r) const { return raw(_c.mul(v, r.v)); }
    MyType operator/=(MyType r){ return v = _c.mul(v, _c.inv(r.v)); }
    MyType operator/(MyType r) const { return raw(_c.mul(v, _c.inv(r.v))); }
    MyType inv() const { return raw(_c.inv(v)); }
    MyType pow(unsigned long long r) const { return raw(_c.pow(v, r)); }
    MyType mulAdd(MyType mul, MyType add) const { return raw(_c.muladd(v, mul.v, add.v)); }
    Int val() const { return v; }
    Int operator*() const { return v; }
    static Int mod(){ return _c.getMod(); }
};

template<unsigned int IDENTIFER, class IDENTIFER2>
DynamicModSupplier DynamicModint<IDENTIFER, IDENTIFER2>::_c;

} // namespace nachia
using Modint = nachia::DynamicModint<1>;

using Mat = array<array<Modint, 2>, 2>;
Mat matmul(Mat l, Mat r){
    Mat res;
    rep(i,2) rep(j,2) rep(k,2) res[i][k] += l[i][j] * r[j][k];
    return res;
}
Modint det(Mat B){
    return B[0][0] * B[1][1] - B[0][1] * B[1][0];
}
bool eq(Mat A, Mat B){
    rep(i,2) rep(j,2) if(A[i][j].val() != B[i][j].val()) return false;
    return true;
}
Mat inv(Mat A){
    auto d = det(A).inv();
    swap(A[0][0], A[1][1]);
    A[0][1] *= Modint(-1);
    A[1][0] *= Modint(-1);
    rep(t,2) rep(s,2) A[t][s] *= d;
    return A;
}

i64 subsolve(Mat A, Mat B){
    Mat id; id[0][0] = id[1][1] = 1;
    Mat Ax = id;
    i64 x = 0;
    while(!eq(Ax, B) && x < 500000){ Ax = matmul(Ax, A); x++; }
    if(x >= 500000) x = -1;
    return x;
}

void testcase(){
    int P; cin >> P; Modint::setMod(P);
    Mat A, B;
    rep(i,2) rep(j,2){ int a; cin >> a; A[i][j] = a; }
    rep(i,2) rep(j,2){ int a; cin >> a; B[i][j] = a; }
    if(det(A).val() == 0){
        cout << subsolve(A, B) << "\n";
        return;
    }
    Modint detB = det(B);
    Mat id; id[0][0] = id[1][1] = 1;
    Mat IA = id; i64 IAp = 0;
    do{ IAp++; IA = matmul(IA, A); } while(det(IA).val() != 1);
    Mat invA = inv(A);

    i64 ans = 0;
    while(det(B).val() != 1 && ans < 500000){ B = matmul(invA, B); ans++; }
    if(ans >= 500000){ cout << "-1\n"; return; }

    i64 ans2 = subsolve(IA, B);
    if(ans2 < 0){ cout << "-1\n"; return; }
    ans += ans2 * IAp;
    cout << ans << "\n";
}

int main(){
    ios::sync_with_stdio(false); cin.tie(nullptr);
    int N; cin >> N;
    rep(i,N) testcase();
    return 0;
}
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