#886081 (C++17) No.2365 Present of good number

提出ソース

結果

問題	No.2365 Present of good number
ユーザー	siganai
提出日時	2023-06-30 22:25:09
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	2 ms / 2,000 ms
コード長	15,410 bytes
コンパイル時間	2,882 ms
コンパイル使用メモリ	232,104 KB
実行使用メモリ	6,948 KB
最終ジャッジ日時	2024-07-07 10:15:41
合計ジャッジ時間	3,142 ms
ジャッジサーバーID （参考情報）	judge2 / judge5

このコードへのチャレンジ
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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	AC	1 ms 6,812 KB
testcase_01	AC	2 ms 6,940 KB
testcase_02	AC	1 ms 6,940 KB
testcase_03	AC	1 ms 6,940 KB
testcase_04	AC	1 ms 6,944 KB
testcase_05	AC	2 ms 6,940 KB
testcase_06	AC	2 ms 6,940 KB
testcase_07	AC	2 ms 6,944 KB
testcase_08	AC	1 ms 6,940 KB
testcase_09	AC	2 ms 6,944 KB
testcase_10	AC	2 ms 6,944 KB
testcase_11	AC	2 ms 6,944 KB
testcase_12	AC	2 ms 6,940 KB
testcase_13	AC	2 ms 6,940 KB
testcase_14	AC	1 ms 6,940 KB
testcase_15	AC	2 ms 6,940 KB
testcase_16	AC	1 ms 6,948 KB
testcase_17	AC	2 ms 6,940 KB
testcase_18	AC	2 ms 6,940 KB
testcase_19	AC	1 ms 6,944 KB
testcase_20	AC	1 ms 6,944 KB
testcase_21	AC	1 ms 6,940 KB
testcase_22	AC	1 ms 6,940 KB
testcase_23	AC	1 ms 6,940 KB
testcase_24	AC	2 ms 6,940 KB
testcase_25	AC	2 ms 6,940 KB
testcase_26	AC	1 ms 6,940 KB
testcase_27	AC	1 ms 6,944 KB
testcase_28	AC	2 ms 6,940 KB
testcase_29	AC	2 ms 6,940 KB
testcase_30	AC	1 ms 6,940 KB
testcase_31	AC	1 ms 6,940 KB
testcase_32	AC	2 ms 6,940 KB
testcase_33	AC	2 ms 6,940 KB
testcase_34	AC	1 ms 6,944 KB
testcase_35	AC	1 ms 6,944 KB
testcase_36	AC	2 ms 6,944 KB
testcase_37	AC	1 ms 6,944 KB
testcase_38	AC	2 ms 6,944 KB
testcase_39	AC	2 ms 6,944 KB
testcase_40	AC	2 ms 6,940 KB

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

raw source code

#line 1 "main.cpp"
//#pragma GCC target("avx")
//#pragma GCC optimize("O3")
//#pragma GCC optimize("unroll-loops")
#include<bits/stdc++.h>
#ifdef LOCAL
#include <debug.hpp>
#define debug(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__)
#else
#define debug(...) (static_cast<void>(0))
#endif
using namespace std;
using ll = long long;
using ld = long double;
using pll = pair<ll, ll>;
using pii = pair<int, int>;
using vi = vector<int>;
using vvi = vector<vi>;
using vvvi = vector<vvi>;
using vl = vector<ll>;
using vvl = vector<vl>;
using vvvl = vector<vvl>;
using vpii = vector<pii>;
using vpll = vector<pll>;
using vs = vector<string>;
template<class T> using pq = priority_queue<T, vector<T>, greater<T>>;
#define overload4(_1, _2, _3, _4, name, ...) name
#define overload3(a,b,c,name,...) name
#define rep1(n) for (ll UNUSED_NUMBER = 0; UNUSED_NUMBER < (n); ++UNUSED_NUMBER)
#define rep2(i, n) for (ll i = 0; i < (n); ++i)
#define rep3(i, a, b) for (ll i = (a); i < (b); ++i)
#define rep4(i, a, b, c) for (ll i = (a); i < (b); i += (c))
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)
#define rrep1(n) for(ll i = (n) - 1;i >= 0;i--)
#define rrep2(i,n) for(ll i = (n) - 1;i >= 0;i--)
#define rrep3(i,a,b) for(ll i = (b) - 1;i >= (a);i--)
#define rrep4(i,a,b,c) for(ll i = (a) + ((b)-(a)-1) / (c) * (c);i >= (a);i -= c)
#define rrep(...) overload4(__VA_ARGS__, rrep4, rrep3, rrep2, rrep1)(__VA_ARGS__)
#define all1(i) begin(i) , end(i)
#define all2(i,a) begin(i) , begin(i) + a
#define all3(i,a,b) begin(i) + a , begin(i) + b
#define all(...) overload3(__VA_ARGS__, all3, all2, all1)(__VA_ARGS__)
#define sum(...) accumulate(all(__VA_ARGS__),0LL)
template<class T> bool chmin(T &a, const T &b){ if(a > b){ a = b; return 1; } else return 0; }
template<class T> bool chmax(T &a, const T &b){ if(a < b){ a = b; return 1; } else return 0; }
template<class T> auto min(const T& a){return *min_element(all(a));}
template<class T> auto max(const T& a){return *max_element(all(a));}
template<class... Ts> void in(Ts&... t);
#define INT(...) int __VA_ARGS__; in(__VA_ARGS__)
#define LL(...) ll __VA_ARGS__; in(__VA_ARGS__)
#define STR(...) string __VA_ARGS__; in(__VA_ARGS__)
#define CHR(...) char __VA_ARGS__; in(__VA_ARGS__)
#define DBL(...) double __VA_ARGS__; in(__VA_ARGS__)
#define LD(...) ld __VA_ARGS__; in(__VA_ARGS__)
#define VEC(type, name, size) vector<type> name(size); in(name)
#define VV(type, name, h, w) vector<vector<type>> name(h, vector<type>(w)); in(name)
ll intpow(ll a, ll b){ ll ans = 1; while(b){if(b & 1) ans *= a; a *= a; b /= 2;} return ans;}
ll modpow(ll a, ll b, ll p){ ll ans = 1; a %= p;if(a < 0) a += p;while(b){ if(b & 1) (ans *= a) %= p; (a *= a) %= p; b /= 2; } return ans; }
ll GCD(ll a,ll b) { if(a == 0 || b == 0) return 0; if(a % b == 0) return b; else return GCD(b,a%b);}
ll LCM(ll a,ll b) { if(a == 0) return b; if(b == 0) return a;return a / GCD(a,b) * b;}
namespace IO{
#define VOID(a) decltype(void(a))
struct setting{ setting(){cin.tie(nullptr); ios::sync_with_stdio(false);fixed(cout); cout.precision(12);}} setting;
template<int I> struct P : P<I-1>{};
template<> struct P<0>{};
template<class T> void i(T& t){ i(t, P<3>{}); }
void i(vector<bool>::reference t, P<3>){ int a; i(a); t = a; }
template<class T> auto i(T& t, P<2>) -> VOID(cin >> t){ cin >> t; }
template<class T> auto i(T& t, P<1>) -> VOID(begin(t)){ for(auto&& x : t) i(x); }
template<class T, size_t... idx> void ituple(T& t, index_sequence<idx...>){
    in(get<idx>(t)...);}
template<class T> auto i(T& t, P<0>) -> VOID(tuple_size<T>{}){
    ituple(t, make_index_sequence<tuple_size<T>::value>{});}
#undef VOID
}
#define unpack(a) (void)initializer_list<int>{(a, 0)...}
template<class... Ts> void in(Ts&... t){ unpack(IO :: i(t)); }
#undef unpack
static const double PI = 3.1415926535897932;
template <class F> struct REC {
    F f;
    REC(F &&f_) : f(forward<F>(f_)) {}
    template <class... Args> auto operator()(Args &&...args) const { return f(*this, forward<Args>(args)...); }};
constexpr int mod = 1000000007;
//constexpr int mod = 998244353;
#line 2 "library/modint/Modint.hpp"
template <int mod>
struct Modint{
    int x;
    Modint():x(0) {}
    Modint(long long y): x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}
    Modint &operator += (const Modint &p) {
        if((x += p.x) >= mod) x -= mod;
        return *this;}
    Modint &operator -= (const Modint &p) {
        if ((x += mod - p.x) >= mod) x -= mod;
        return *this;}
    Modint &operator *= (const Modint &p) {
        x = (int)(1LL * x * p.x % mod);
        return *this;}
    Modint &operator /= (const Modint &p) {
        *this *= p.inverse();
        return *this;}
    Modint operator -() const{return Modint(-x);}
    Modint operator +(const Modint &p) const {return Modint(*this) += p;}
    Modint operator -(const Modint &p) const {return Modint(*this) -= p;}
    Modint operator *(const Modint &p) const {return Modint(*this) *= p;}
    Modint operator /(const Modint &p) const {return Modint(*this) /= p;}
    Modint &operator ++() {if(x == mod - 1) x = 0; else x++; return *this;}
    Modint &operator --() {if(x == 0) x = mod - 1; else x--; return *this;} 
    bool operator == (const Modint &p) const {return x == p.x;}
    bool operator != (const Modint &p) const {return x != p.x;}
    Modint inverse() const {
        int a = x, b = mod, u = 1, v = 0, t;
        while (b > 0) {
            t = a / b;
            swap(a -= t * b, b);
            swap(u -= t * v, v);
        }
        return Modint(u);}
    Modint pow(long long n) const {
        Modint ret(1), mul(x);
        while (n > 0) {
            if (n & 1) ret *= mul;
            mul *= mul;
            n >>= 1;
        }
        return ret;}
    friend ostream &operator<<(ostream &os, const Modint &p) { return os << p.x; }
    friend istream &operator>>(istream &is, Modint &a) {
        long long t;
        is >> t;
        a = Modint<mod>(t);
        return (is);
    }
    int get() const { return x; }
    static constexpr int get_mod() {return mod;}
};
#line 2 "library/modint/barrett-reduction.hpp"
struct Barrett {
    using u32 = unsigned int;
    using i64 = long long;
    using u64 = unsigned long long;
    u32 m;
    u64 im;
    Barrett() : m(), im() {}
    Barrett(int n) : m(n), im(u64(-1) / m + 1) {}
    constexpr inline i64 quo(u64 n) {
        u64 x = u64((__uint128_t(n) * im) >> 64);
        u32 r = n - x * m;
        return m <= r ? x - 1 : x;
    }
    constexpr inline i64 rem(u64 n) {
        u64 x = u64((__uint128_t(n) * im) >> 64);
        u32 r = n - x * m;
        return m <= r ? r + m : r;
    }
    constexpr inline pair<i64, int> quorem(u64 n) {
        u64 x = u64((__uint128_t(n) * im) >> 64);
        u32 r = n - x * m;
        if (m <= r) return {x - 1, r + m};
        return {x, r};
    }
    constexpr inline i64 pow(u64 n, i64 p) {
        u32 a = rem(n), r = m == 1 ? 0 : 1;
        while (p) {
            if (p & 1) r = rem(u64(r) * a);
            a = rem(u64(a) * a);
            p >>= 1;
        }
        return r;
    }
};
#line 3 "library/modint/ArbitaryModint.hpp"
struct ArbitraryModint {
    int x;
    ArbitraryModint():x(0) {}
    ArbitraryModint(int64_t y) {
        int z = y % get_mod();
        if(z < 0) z += get_mod();
        x = z;
    }
    ArbitraryModint &operator+=(const ArbitraryModint &p) {
        if((x += p.x) >= get_mod()) x -= get_mod();
        return *this;
    }
    ArbitraryModint &operator-=(const ArbitraryModint &p) {
        if((x += get_mod() - p.x) >= get_mod()) x -= get_mod();
        return *this;
    }
    ArbitraryModint &operator*=(const ArbitraryModint &p) {
        x = rem((unsigned long long)x * p.x);
        return *this;
    }
    ArbitraryModint &operator/=(const ArbitraryModint &p) {
        *this *= p.inverse();
        return *this;
    }
    ArbitraryModint operator-() const {return ArbitraryModint(-x);};
    ArbitraryModint operator+(const ArbitraryModint &p) const{
        return ArbitraryModint(*this) += p;
    }
    ArbitraryModint operator-(const ArbitraryModint &p) const{
        return ArbitraryModint(*this) -= p;
    }
    ArbitraryModint operator*(const ArbitraryModint &p) const{
        return ArbitraryModint(*this) *= p;
    }
    ArbitraryModint operator/(const ArbitraryModint &p) const {
        return ArbitraryModint(*this) /= p;
    }
    bool operator==(const ArbitraryModint &p) {return x == p.x;}
    bool operator!=(const ArbitraryModint &p) {return x != p.x;}
    ArbitraryModint inverse() const {
        int a = x,b = get_mod(),u = 1,v = 0,t;
        while(b > 0) {
            t = a / b;
            swap(a -= t * b,b);
            swap(u -= t * v,v);
        }
        return ArbitraryModint(u);
    }
    ArbitraryModint pow(int64_t n) const {
        ArbitraryModint ret(1),mul(x);
        while(n > 0) {
            if(n & 1) ret *= mul;
            mul *= mul;
            n >>= 1;
        }
        return ret;
    }
    friend ostream &operator<<(ostream &os,const ArbitraryModint &p) {
        return os << p.x;
    }
    friend istream &operator>>(istream &is,ArbitraryModint &a) {
        int64_t t;
        is >> t;
        a = ArbitraryModint(t);
        return (is);
    }
    int get() const {return x;}
    inline unsigned int rem(unsigned long long p) {return barrett().rem(p);};
    static inline Barrett &barrett() {
        static Barrett b;
        return b;
    }
    static inline int &get_mod() {
        static int mod = 0;
        return mod;
    }
    static void set_mod(int md) {
        assert(0 < md && md <= (1LL << 30) - 1);
        get_mod() = md;
        barrett() = Barrett(md);
    }
};
#line 87 "main.cpp"
using nmint = ArbitraryModint;
using mint = Modint<mod>;
using vm = vector<mint>;
using vvm = vector<vm>;
using vvvm = vector<vvm>;
#line 2 "library/math/factorize.hpp"
vector<pair<long long,int>> prime_factorization(long long n) {
    vector<pair<long long,int>> ret;
    int c = 0;
    while(n % 2 == 0) {
        c++;
        n >>= 1;
    }
    if(c) ret.emplace_back(2,c);
    for(long long i = 3; i * i <= n; i += 2) {
        c = 0;
        while(n % i == 0) {
            n /= i;
            c++;
        }
        if(c) ret.emplace_back(i,c);
    }
    if (n != 1) ret.emplace_back(n,1);
    return ret;
}
vector<long long> divisor(long long n) {
    vector<long long> ret;
    for(long long i = 1; i * i <= n; i++) {
        if (n % i == 0) {
            ret.push_back(i);
            if(i * i != n) {ret.push_back(n / i);}
        }
    }
    sort(ret.begin(),ret.end());
    return ret;
}
#line 2 "library/matrix/matrix.hpp"
template <class T>
struct Matrix {
    vector<vector<T>> A;
    Matrix() = default;
    Matrix(int n, int m) : A(n, vector<T>(m, T())) {}
    Matrix(int n) : A(n, vector<T>(n, T())){};
    int H() const { return A.size(); }
    int W() const { return A[0].size(); }
    int size() const { return A.size(); }
    inline const vector<T> &operator[](int k) const { return A[k]; }
    inline vector<T> &operator[](int k) { return A[k]; }
    static Matrix I(int n) {
        Matrix mat(n);
        for (int i = 0; i < n; i++) mat[i][i] = 1;
        return (mat);
    }
    Matrix &operator+=(const Matrix &B) {
        int n = H(), m = W();
        assert(n == B.H() && m == B.W());
        for (int i = 0; i < n; i++) for (int j = 0; j < m; j++) (*this)[i][j] += B[i][j];
        return (*this);
    }
    Matrix &operator-=(const Matrix &B) {
        int n = H(), m = W();
        assert(n == B.H() && m == B.W());
        for (int i = 0; i < n; i++) for (int j = 0; j < m; j++) (*this)[i][j] -= B[i][j];
        return (*this);
    }
    Matrix &operator*=(const Matrix &B) {
        int n = H(), m = B.W(), p = W();
        assert(p == B.H());
        vector<vector<T>> C(n, vector<T>(m, T{}));
        for (int i = 0; i < n; i++)
            for (int k = 0; k < p; k++)
                for (int j = 0; j < m; j++) C[i][j] += (*this)[i][k] * B[k][j];
        A.swap(C);
        return (*this);
    }
    Matrix &operator^=(long long k) {
        Matrix B = Matrix::I(H());
        while (k > 0) {
            if (k & 1) B *= *this;
            *this *= *this;
            k >>= 1LL;
        }
        A.swap(B.A);
        return (*this);
    }
    Matrix operator+(const Matrix &B) const { return (Matrix(*this) += B); }
    Matrix operator-(const Matrix &B) const { return (Matrix(*this) -= B); }
    Matrix operator*(const Matrix &B) const { return (Matrix(*this) *= B); }
    Matrix operator^(const long long k) const { return (Matrix(*this) ^= k); }
    bool operator==(const Matrix &B) const {
        assert(H() == B.H() && W() == B.W());
        for (int i = 0; i < H(); i++) for (int j = 0; j < W(); j++) {
            if (A[i][j] != B[i][j]) return false;
        }
        return true;
    }
    bool operator!=(const Matrix &B) const {
        assert(H() == B.H() && W() == B.W());
        for (int i = 0; i < H(); i++) for (int j = 0; j < W(); j++) {
            if (A[i][j] != B[i][j]) return true;
        }
        return false;
    }
    friend ostream &operator<<(ostream &os, const Matrix &p) {
        int n = p.H(), m = p.W();
        for (int i = 0; i < n; i++) {
            os << (i ? "   " : "") << "[";
            for (int j = 0; j < m; j++) {
                os << p[i][j] << (j + 1 == m ? "]\n" : ",");
            }
        }
        return (os);
    }
    T determinant() const {
        Matrix B(*this);
        assert(H() == W());
        T ret = 1;
        for (int i = 0; i < H(); i++) {
            int idx = -1;
            for (int j = i; j < W(); j++) {
                if (B[j][i] != 0) {
                    idx = j;
                    break;
                }
            }
            if (idx == -1) return 0;
            if (i != idx) {
                ret *= T(-1);
                swap(B[i], B[idx]);
            }
            ret *= B[i][i];
            T inv = T(1) / B[i][i];
            for (int j = 0; j < W(); j++) {
                B[i][j] *= inv;
            }
            for (int j = i + 1; j < H(); j++) {
                T a = B[j][i];
                if (a == 0) continue;
                for (int k = i; k < W(); k++) {
                    B[j][k] -= B[i][k] * a;
                }
            }
        }
        return ret;
    }
};
#line 94 "main.cpp"
int main() {
    nmint::set_mod(mod - 1);
    INT(n);
    LL(k);
    auto ret = prime_factorization(n);
    vector<pair<int,nmint>> A;
    for(auto &[p,c]:ret) A.emplace_back(p,c);
    while(A.back().first > 3 && k > 0) {
        map<int,nmint> mp;
        for(auto &[p,c]:A) {
            auto tmp = prime_factorization(p + 1);
            for(auto &[pp,cc]:tmp) {
                mp[pp] += c * cc;
            }
        }
        A.clear();
        for(auto &x:mp) {
            A.emplace_back(x);
        }
        k--;
    }
    if(k == 0) {
        mint ans = 1;
        for(auto &[p,c]:A) {
            ans *= mint(p).pow(c.x);
        }
        cout << ans << '\n';
        return 0;
    }
    Matrix<nmint> mat(2);
    mat[0][1] = 1;
    mat[1][0] = 2;
    mat ^= k;
    vector<nmint> b(2);
    for(auto &[p,c]:A) {
        b[p-2] = c;
    }
    vector<nmint> cnt(2);
    rep(i,2) {
        rep(j,2) {
            cnt[i] += b[j] * mat[j][i];
        }
    }
    mint ans = 1;
    rep(i,2) ans *= mint(i+2).pow(cnt[i].x);
    cout << ans << '\n';
}

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結果

テストケース

ソースコード