結果

問題 No.2365 Present of good number
コンテスト
ユーザー ebi_fly
提出日時 2023-07-01 00:59:48
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 258 ms / 2,000 ms
コード長 8,794 bytes
コンパイル時間 1,936 ms
コンパイル使用メモリ 149,984 KB
最終ジャッジ日時 2025-02-15 04:51:59
ジャッジサーバーID
（参考情報） 		judge2 / judge1
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 * 39
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 # 

#line 1 "a.cpp"
#include <algorithm>
#include <bitset>
#include <cassert>
#include <chrono>
#include <climits>
#include <cmath>
#include <complex>
#include <cstddef>
#include <cstdint>
#include <cstdlib>
#include <cstring>
#include <functional>
#include <iomanip>
#include <iostream>
#include <limits>
#include <map>
#include <memory>
#include <numeric>
#include <optional>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

/* macro */

#define rep(i, a, n) for (int i = (int)(a); i < (int)(n); i++)
#define rrep(i, a, n) for (int i = ((int)(n)-1); i >= (int)(a); i--)
#define Rep(i, a, n) for (i64 i = (i64)(a); i < (i64)(n); i++)
#define RRep(i, a, n) for (i64 i = ((i64)(n)-i64(1)); i >= (i64)(a); i--)
#define all(v) (v).begin(), (v).end()
#define rall(v) (v).rbegin(), (v).rend()

/* macro end */

/* template */

namespace ebi {

#ifdef LOCAL
#define debug(...)                                                      \
    std::cerr << "LINE: " << __LINE__ << "  [" << #__VA_ARGS__ << "]:", \
        debug_out(__VA_ARGS__)
#else
#define debug(...)
#endif

void debug_out() {
    std::cerr << std::endl;
}

template <typename Head, typename... Tail> void debug_out(Head h, Tail... t) {
    std::cerr << " " << h;
    if (sizeof...(t) > 0) std::cerr << " :";
    debug_out(t...);
}

template <typename T1, typename T2>
std::ostream &operator<<(std::ostream &os, const std::pair<T1, T2> &pa) {
    return os << pa.first << " " << pa.second;
}

template <typename T1, typename T2>
std::istream &operator>>(std::istream &os, std::pair<T1, T2> &pa) {
    return os >> pa.first >> pa.second;
}

template <typename T>
std::ostream &operator<<(std::ostream &os, const std::vector<T> &vec) {
    for (std::size_t i = 0; i < vec.size(); i++)
        os << vec[i] << (i + 1 == vec.size() ? "" : " ");
    return os;
}

template <typename T>
std::istream &operator>>(std::istream &os, std::vector<T> &vec) {
    for (T &e : vec) std::cin >> e;
    return os;
}

template <typename T>
std::ostream &operator<<(std::ostream &os, const std::optional<T> &opt) {
    if (opt) {
        os << opt.value();
    } else {
        os << "invalid value";
    }
    return os;
}

using std::size_t;
using i32 = std::int32_t;
using u32 = std::uint32_t;
using i64 = std::int64_t;
using u64 = std::uint64_t;
using i128 = __int128_t;
using u128 = __uint128_t;

template <class T> inline bool chmin(T &a, T b) {
    if (a > b) {
        a = b;
        return true;
    }
    return false;
}

template <class T> inline bool chmax(T &a, T b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}

template <class T> T pow(T x, i64 n) {
    T res = 1;
    while (n > 0) {
        if (n & 1) res = res * x;
        x = x * x;
        n >>= 1;
    }
    return res;
}

template <class T> struct Edge {
    int to;
    T cost;
    Edge(int _to, T _cost = 1) : to(_to), cost(_cost) {}
};

template <class T> struct Graph : std::vector<std::vector<Edge<T>>> {
    using std::vector<std::vector<Edge<T>>>::vector;
    void add_edge(int u, int v, T w, bool directed = false) {
        (*this)[u].emplace_back(v, w);
        if (directed) return;
        (*this)[v].emplace_back(u, w);
    }
};

struct graph : std::vector<std::vector<int>> {
    using std::vector<std::vector<int>>::vector;
    void add_edge(int u, int v, bool directed = false) {
        (*this)[u].emplace_back(v);
        if (directed) return;
        (*this)[v].emplace_back(u);
    }
};

constexpr i64 LNF = std::numeric_limits<i64>::max() / 4;

constexpr int INF = std::numeric_limits<int>::max() / 2;

const std::vector<int> dy = {1, 0, -1, 0, 1, 1, -1, -1};
const std::vector<int> dx = {0, 1, 0, -1, 1, -1, 1, -1};

}  // namespace ebi

#line 2 "math/linear_sieve.hpp"

#line 2 "utility/int_alias.hpp"

#line 5 "utility/int_alias.hpp"

using std::size_t;
using i8 = std::int8_t;
using u8 = std::uint8_t;
using i16 = std::int16_t;
using u16 = std::uint16_t;
using i32 = std::int32_t;
using u32 = std::uint32_t;
using i64 = std::int64_t;
using u64 = std::uint64_t;
using i128 = __int128_t;
using u128 = __uint128_t;
#line 4 "math/linear_sieve.hpp"

/*
    reference: https://37zigen.com/linear-sieve/
    verify:    https://atcoder.jp/contests/abc162/submissions/25095562
*/

#line 11 "math/linear_sieve.hpp"

namespace ebi {

struct linear_sieve {
  private:
    using u64 = std::uint64_t;
    int n;
    std::vector<int> sieve;
    std::vector<int> prime;

  public:
    linear_sieve(int _n) : n(_n), sieve(std::vector<int>(_n + 1, -1)) {
        for (int i = 2; i <= n; i++) {
            if (sieve[i] < 0) {
                sieve[i] = i;
                prime.emplace_back(i);
            }
            for (auto p : prime) {
                if (u64(p) * u64(i) > u64(n) || p > sieve[i]) break;
                sieve[p * i] = p;
            }
        }
    }

    std::vector<int> prime_table() {
        return prime;
    }

    std::vector<std::pair<int, int>> factorize(int n) {
        std::vector<std::pair<int, int>> res;
        while (n > 1) {
            int p = sieve[n];
            int exp = 0;
            if (p < 0) {
                res.emplace_back(n, 1);
                break;
            }
            while (sieve[n] == p) {
                n /= p;
                exp++;
            }
            res.emplace_back(p, exp);
        }
        return res;
    }

    std::vector<int> divisors(int n) {
        std::vector<int> res;
        res.emplace_back(1);
        auto pf = factorize(n);
        for (auto p : pf) {
            int sz = res.size();
            for (int i = 0; i < sz; i++) {
                int ret = 1;
                for (int j = 0; j < p.second; j++) {
                    ret *= p.first;
                    res.emplace_back(res[i] * ret);
                }
            }
        }
        return res;
    }

    template <class T> std::vector<T> fast_zeta(const std::vector<T> &f) {
        std::vector<T> F = f;
        int sz = f.size();
        assert(sz <= n + 1);
        for (int i = 2; i < sz; i++) {
            if (sieve[i] != i) continue;
            for (int j = (sz - 1) / i; j >= 1; j--) {
                F[j] += F[j * i];
            }
        }
        return F;
    }

    template <class T> std::vector<T> fast_mobius(const std::vector<T> &F) {
        std::vector<T> f = F;
        int sz = F.size();
        assert(sz <= n + 1);
        for (int i = 2; i < sz; i++) {
            if (sieve[i] != i) continue;
            for (int j = 1; j * i < sz; j++) {
                f[j] -= f[j * i];
            }
        }
        return f;
    }

    template <class modint> std::vector<modint> pow_table(int k) {
        std::vector<modint> table(n + 1, 1);
        table[0] = 0;
        for (int i = 2; i <= n; i++) {
            if (sieve[i] == i) {
                table[i] = modint(i).pow(k);
                continue;
            }
            table[i] = table[sieve[i]] * table[i / sieve[i]];
        }
        return table;
    }

    template <class modint> std::vector<modint> inv_table() {
        return pow_table(modint::mod() - 2);
    }
};

}  // namespace ebi
#line 166 "a.cpp"

#include <atcoder/modint>

namespace ebi {

using mint = atcoder::modint1000000007;
using dmint = atcoder::dynamic_modint<0>;

void main_() {
    int n;
    i64 k;
    std::cin >> n >> k;
    int max = 200000;
    linear_sieve sieve(max);
    auto ptable = sieve.prime_table();
    int sz = ptable.size();
    std::vector<int> inv_ptable(max, -1);
    rep(i,0,sz) inv_ptable[ptable[i]] = i;
    dmint::set_mod(mint::mod() - 1);
    std::vector a(60, std::vector<dmint>(sz));
    for(auto [p, c]: sieve.factorize(n)) a[0][inv_ptable[p]] = c;
    rep(i,0,60-1) {
        rep(j,0,sz) {
            for(auto [p,c]: sieve.factorize(ptable[j] + 1)) {
                a[i+1][inv_ptable[p]] += c * a[i][j];
            }
        }
    }
    if(k < 60) {
        mint ans = 1;
        rep(i,0,sz) ans *= mint(ptable[i]).pow(a[k][i].val());
        std::cout << ans.val() << '\n';
    }
    else {
        k -= 59;
        std::vector<dmint> res(2);
        res[0] = a[59][0] * dmint(2).pow(k >> 1);
        res[1] = a[59][1] * dmint(2).pow(k >> 1);
        if(k & 1) {
            std::swap(res[0], res[1]);
            res[0] *= 2;
        }
        mint ans = mint(2).pow(res[0].val()) * mint(3).pow(res[1].val());
        std::cout << ans.val() << '\n';
    }
}

}  // namespace ebi

int main() {
    std::cout << std::fixed << std::setprecision(15);
    std::cin.tie(nullptr);
    std::ios::sync_with_stdio(false);
    int t = 1;
    // std::cin >> t;
    while (t--) {
        ebi::main_();
    }
    return 0;
}
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