結果

問題 No.1973 Divisor Sequence
ユーザー apricityapricity
提出日時 2023-03-25 10:58:37
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 12 ms / 2,000 ms
コード長 6,904 bytes
コンパイル時間 1,393 ms
コンパイル使用メモリ 145,772 KB
実行使用メモリ 5,376 KB
最終ジャッジ日時 2024-09-18 18:25:43
合計ジャッジ時間 2,420 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge1
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 2 ms
5,248 KB
testcase_01 AC 1 ms
5,376 KB
testcase_02 AC 7 ms
5,376 KB
testcase_03 AC 5 ms
5,376 KB
testcase_04 AC 7 ms
5,376 KB
testcase_05 AC 9 ms
5,376 KB
testcase_06 AC 5 ms
5,376 KB
testcase_07 AC 8 ms
5,376 KB
testcase_08 AC 8 ms
5,376 KB
testcase_09 AC 6 ms
5,376 KB
testcase_10 AC 8 ms
5,376 KB
testcase_11 AC 5 ms
5,376 KB
testcase_12 AC 8 ms
5,376 KB
testcase_13 AC 4 ms
5,376 KB
testcase_14 AC 9 ms
5,376 KB
testcase_15 AC 6 ms
5,376 KB
testcase_16 AC 7 ms
5,376 KB
testcase_17 AC 9 ms
5,376 KB
testcase_18 AC 9 ms
5,376 KB
testcase_19 AC 10 ms
5,376 KB
testcase_20 AC 9 ms
5,376 KB
testcase_21 AC 10 ms
5,376 KB
testcase_22 AC 6 ms
5,376 KB
testcase_23 AC 12 ms
5,376 KB
testcase_24 AC 4 ms
5,376 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

diff # 

#include<iostream>
#include<string>
#include<vector>
#include<algorithm>
#include<numeric>
#include<cmath>
#include<utility>
#include<tuple>
#include<cstdint>
#include<cstdio>
#include<iomanip>
#include<map>
#include<queue>
#include<set>
#include<stack>
#include<deque>
#include<unordered_map>
#include<unordered_set>
#include<bitset>
#include<cctype>
#include<chrono>
#include<random>
#include<cassert>
#include<cstddef>
#include<iterator>
#include<string_view>
#include<type_traits>

#ifdef LOCAL
#  include "debug_print.hpp"
#  define debug(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__)
#else
#  define debug(...) (static_cast<void>(0))
#endif

using namespace std;
#define rep(i,n) for(int i=0; i<(n); i++)
#define rrep(i,n) for(int i=(n)-1; i>=0; i--)
#define FOR(i,a,b) for(int i=(a); i<(b); i++)
#define RFOR(i,a,b) for(int i=(b-1); i>=(a); i--)
#define ALL(v) v.begin(), v.end()
#define RALL(v) v.rbegin(), v.rend()
#define UNIQUE(v) v.erase( unique(v.begin(), v.end()), v.end() );
#define pb push_back
using ll = long long;
using D = double;
using LD = long double;
using P = pair<int, int>;
template<typename T> using PQ = priority_queue<T,vector<T>>;
template<typename T> using minPQ = priority_queue<T, vector<T>, greater<T>>;
template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return 1; } return 0; }
void yesno(bool flag) {cout << (flag?"Yes":"No") << "\n";}

template<typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
    os << p.first << " " << p.second;
    return os;
}
template<typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p) {
    is >> p.first >> p.second;
    return is;
}

template<typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
    int s = (int)v.size();
    for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
    return os;
}
template<typename T>
istream &operator>>(istream &is, vector<T> &v) {
    for (auto &x : v) is >> x;
    return is;
}
void in() {}
template<typename T, class... U>
void in(T &t, U &...u) {
    cin >> t;
    in(u...);
}
void out() { cout << "\n"; }
template<typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u) {
    cout << t;
    if (sizeof...(u)) cout << sep;
    out(u...);
}
void outr() {}
template<typename T, class... U, char sep = ' '>
void outr(const T &t, const U &...u) {
    cout << t;
    outr(u...);
}

template<int mod> struct Fp {
    long long val;
    constexpr Fp(long long v = 0) noexcept : val(v % mod) {
        if (val < 0) val += mod;
    }
    constexpr int getmod() { return mod; }
    constexpr Fp operator - () const noexcept {
        return val ? mod - val : 0;
    }
    constexpr Fp operator + (const Fp& r) const noexcept { return Fp(*this) += r; }
    constexpr Fp operator - (const Fp& r) const noexcept { return Fp(*this) -= r; }
    constexpr Fp operator * (const Fp& r) const noexcept { return Fp(*this) *= r; }
    constexpr Fp operator / (const Fp& r) const noexcept { return Fp(*this) /= r; }
    constexpr Fp& operator += (const Fp& r) noexcept {
        val += r.val;
        if (val >= mod) val -= mod;
        return *this;
    }
    constexpr Fp& operator -= (const Fp& r) noexcept {
        val -= r.val;
        if (val < 0) val += mod;
        return *this;
    }
    constexpr Fp& operator *= (const Fp& r) noexcept {
        val = val * r.val % mod;
        return *this;
    }
    constexpr Fp& operator /= (const Fp& r) noexcept {
        long long a = r.val, b = mod, u = 1, v = 0;
        while (b) {
            long long t = a / b;
            a -= t * b; swap(a, b);
            u -= t * v; swap(u, v);
        }
        val = val * u % mod;
        if (val < 0) val += mod;
        return *this;
    }
    constexpr bool operator == (const Fp& r) const noexcept {
        return this->val == r.val;
    }
    constexpr bool operator != (const Fp& r) const noexcept {
        return this->val != r.val;
    }
    friend constexpr istream& operator >> (istream &is, const Fp<mod>& x) noexcept {
        int val; is >> val;
        x = Fp<mod>(val);
        return is;
    }
    friend constexpr ostream& operator << (ostream &os, const Fp<mod>& x) noexcept {
        return os << x.val;
    }
    friend constexpr Fp<mod> modpow(const Fp<mod> &a, long long n) noexcept {
        if (n == 0) return 1;
        auto t = modpow(a, n / 2);
        t = t * t;
        if (n & 1) t = t * a;
        return t;
    }
};

const int mod = 1e9+7;
// const int mod = 998244353;
using mint = Fp<mod>;

struct factorizer{
    vector<bool> isprime;
    vector<ll> primes;
    factorizer(ll n) : isprime(sqrtl(n)+1,true){
        isprime[1] = false;
        for(ll i = 2; i*i <= n; i++){
            if(!isprime[i]) continue;
            primes.pb(i);
            for(ll j = i+i; j*j <=n; j += i){
                isprime[j] = false;
            }
        }
    }

    vector<pair<ll,int>> factorize(ll n){
        vector<pair<ll,int>> res;
        for(ll p : primes){
            if(p * p > n) break;
            int e = 0;
            while(n%p == 0){
                n /= p;
                e++;
            }
            if(e > 0) res.pb({p,e});
        }
        if(n > 1) res.pb({n,1});
        return res;
    }

    vector<ll> divisors(ll n){
        vector<ll> res({1});
        const auto& pf = factorize(n);
        for(auto p : pf){
            for(ll x : res){
                ll v = 1;
                rep(j,p.second){
                    v *= p.first;
                    res.pb(x * v);
                }
            }
        }
        return res;
    }
};

template<typename T> struct Matrix{
    int r,c;
    vector<vector<T>> a;
    Matrix(int r, int c, T init = 0) : r(r), c(c), a(r, vector<T>(c, init)) {}
    
    Matrix& unit(){
        assert(r == c);
        rep(i,r) a[i][i] = 1;
        return *this;
    }

    const vector<T>& operator[] (int i) const {return a[i];}
    vector<T>& operator[] (int i) {return a[i];}

    Matrix operator* (const Matrix& b) const{
        assert(c == b.r);
        Matrix res(r, b.c);
        rep(i,r)rep(k,c)rep(j,b.c) res[i][j] += a[i][k] * b[k][j];
        return res;
    }

    Matrix pow(ll k) const{
        assert(r == c);
        Matrix now = *this;
        Matrix res = Matrix(r,c).unit();
        while(k){
            if(k & 1) res = res * now;
            now = now * now;
            k >>= 1;
        }
        return res;
    }
};

using mat = Matrix<mint>;

int main(){
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    ll n,m; in(n,m);
    factorizer f(m+1);
    auto v = f.factorize(m);
    mint ans = 1;

    for(auto [p,e] : v){
        mat x(e+1,e+1);
        rep(i,e+1)rep(j,e+1) if(i+j >= e) x[i][j] = 1;
        x = x.pow(n+1);
        mint tmp = x[e][e];
        ans *= tmp;
    }
    out(ans);
}
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