number/primes_extra.yukicoder-1659.test.cpp

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• Last update: 2021-08-30 04:35:37+09:00
• Problem: https://yukicoder.me/problems/no/1659
• Link: https://github.com/online-judge-tools/template-generator)

Depends on

• combination / 組合せ ${} _ n C _ r$ (愚直 $O(r)$) (modulus/choose_simple.hpp)
• quotient ring / 剰余環 $\mathbb{Z}/n\mathbb{Z}$ (modulus/mint.hpp)
• modulus/modinv.hpp
• modulus/modpow.hpp
• 重複組合せ ${} _ n H _ r = {} _ {n + r - 1} C _ r$ (愚直 $O(r)$) (modulus/multichoose_simple.hpp)
• number/primes.hpp
• number/primes_extra.hpp
• utils/macros.hpp

Code

#define PROBLEM "https://yukicoder.me/problems/no/1659"
#include <iostream>
#include "../utils/macros.hpp"
#include "../modulus/mint.hpp"
#include "../number/primes.hpp"
#include "../number/primes_extra.hpp"
#include "../modulus/multichoose_simple.hpp"
using namespace std;

prepared_primes primes(1e6 + 100);

constexpr int64_t MOD = 1000000007;
mint<MOD> solve(int64_t n, int64_t k) {
    mint<MOD> ans = 1;
    for (auto [p, e] : list_prime_factors_as_map(primes, n)) {
        // ans *= multichoose_simple<MOD>(k, e);
        mint<MOD> y = 0;
        REP (x, e + 1) {
            y += multichoose_simple<MOD>(k, x);
        }
        ans *= y;
    }
    return ans;
}

// generated by oj-template v4.8.0 (https://github.com/online-judge-tools/template-generator)
int main() {
    std::ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
    int64_t N, K;
    std::cin >> N >> K;
    auto ans = solve(N, K);
    std::cout << ans << '\n';
    return 0;
}

#line 1 "number/primes_extra.yukicoder-1659.test.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/1659"
#include <iostream>
#line 2 "utils/macros.hpp"
#define REP(i, n) for (int i = 0; (i) < (int)(n); ++ (i))
#define REP3(i, m, n) for (int i = (m); (i) < (int)(n); ++ (i))
#define REP_R(i, n) for (int i = (int)(n) - 1; (i) >= 0; -- (i))
#define REP3R(i, m, n) for (int i = (int)(n) - 1; (i) >= (int)(m); -- (i))
#define ALL(x) std::begin(x), std::end(x)
#line 2 "modulus/mint.hpp"
#include <cstdint>
#line 2 "modulus/modpow.hpp"
#include <cassert>
#line 4 "modulus/modpow.hpp"

inline int32_t modpow(uint_fast64_t x, uint64_t k, int32_t MOD) {
    assert (/* 0 <= x and */ x < (uint_fast64_t)MOD);
    uint_fast64_t y = 1;
    for (; k; k >>= 1) {
        if (k & 1) (y *= x) %= MOD;
        (x *= x) %= MOD;
    }
    assert (/* 0 <= y and */ y < (uint_fast64_t)MOD);
    return y;
}
#line 2 "modulus/modinv.hpp"
#include <algorithm>
#line 5 "modulus/modinv.hpp"

inline int32_t modinv_nocheck(int32_t value, int32_t MOD) {
    assert (0 <= value and value < MOD);
    if (value == 0) return -1;
    int64_t a = value, b = MOD;
    int64_t x = 0, y = 1;
    for (int64_t u = 1, v = 0; a; ) {
        int64_t q = b / a;
        x -= q * u; std::swap(x, u);
        y -= q * v; std::swap(y, v);
        b -= q * a; std::swap(b, a);
    }
    if (not (value * x + MOD * y == b and b == 1)) return -1;
    if (x < 0) x += MOD;
    assert (0 <= x and x < MOD);
    return x;
}

inline int32_t modinv(int32_t x, int32_t MOD) {
    int32_t y = modinv_nocheck(x, MOD);
    assert (y != -1);
    return y;
}
#line 6 "modulus/mint.hpp"

/**
 * @brief quotient ring / 剰余環 $\mathbb{Z}/n\mathbb{Z}$
 */
template <int32_t MOD>
struct mint {
    int32_t value;
    mint() : value() {}
    mint(int64_t value_) : value(value_ < 0 ? value_ % MOD + MOD : value_ >= MOD ? value_ % MOD : value_) {}
    mint(int32_t value_, std::nullptr_t) : value(value_) {}
    explicit operator bool() const { return value; }
    inline mint<MOD> operator + (mint<MOD> other) const { return mint<MOD>(*this) += other; }
    inline mint<MOD> operator - (mint<MOD> other) const { return mint<MOD>(*this) -= other; }
    inline mint<MOD> operator * (mint<MOD> other) const { return mint<MOD>(*this) *= other; }
    inline mint<MOD> & operator += (mint<MOD> other) { this->value += other.value; if (this->value >= MOD) this->value -= MOD; return *this; }
    inline mint<MOD> & operator -= (mint<MOD> other) { this->value -= other.value; if (this->value <    0) this->value += MOD; return *this; }
    inline mint<MOD> & operator *= (mint<MOD> other) { this->value = (uint_fast64_t)this->value * other.value % MOD; return *this; }
    inline mint<MOD> operator - () const { return mint<MOD>(this->value ? MOD - this->value : 0, nullptr); }
    inline bool operator == (mint<MOD> other) const { return value == other.value; }
    inline bool operator != (mint<MOD> other) const { return value != other.value; }
    inline mint<MOD> pow(uint64_t k) const { return mint<MOD>(modpow(value, k, MOD), nullptr); }
    inline mint<MOD> inv() const { return mint<MOD>(modinv(value, MOD), nullptr); }
    inline mint<MOD> operator / (mint<MOD> other) const { return *this * other.inv(); }
    inline mint<MOD> & operator /= (mint<MOD> other) { return *this *= other.inv(); }
};
template <int32_t MOD> mint<MOD> operator + (int64_t value, mint<MOD> n) { return mint<MOD>(value) + n; }
template <int32_t MOD> mint<MOD> operator - (int64_t value, mint<MOD> n) { return mint<MOD>(value) - n; }
template <int32_t MOD> mint<MOD> operator * (int64_t value, mint<MOD> n) { return mint<MOD>(value) * n; }
template <int32_t MOD> mint<MOD> operator / (int64_t value, mint<MOD> n) { return mint<MOD>(value) / n; }
template <int32_t MOD> std::istream & operator >> (std::istream & in, mint<MOD> & n) { int64_t value; in >> value; n = value; return in; }
template <int32_t MOD> std::ostream & operator << (std::ostream & out, mint<MOD> n) { return out << n.value; }
#line 5 "number/primes.hpp"
#include <vector>
#line 7 "number/primes.hpp"

struct prepared_primes {
    int size;
    std::vector<int> sieve;
    std::vector<int> primes;

    /**
     * @note O(size)
     */
    prepared_primes(int size_)
        : size(size_) {

        sieve.resize(size);
        REP3 (p, 2, size) if (sieve[p] == 0) {
            primes.push_back(p);
            for (int k = p; k < size; k += p) {
                if (sieve[k] == 0) {
                    sieve[k] = p;
                }
            }
        }
    }

    /**
     * @note let k be the length of the result, O(k) if n < size; O(\sqrt{n} + k) if size <= n < size^2
     */
    std::vector<int64_t> list_prime_factors(int64_t n) const {
        assert (1 <= n and n < (int64_t)size * size);
        std::vector<int64_t> result;

        // trial division for large part
        for (int p : primes) {
            if (n < size or n < (int64_t)p * p) {
                break;
            }
            while (n % p == 0) {
                n /= p;
                result.push_back(p);
            }
        }

        // small part
        if (n == 1) {
            // nop
        } else if (n < size) {
            while (n != 1) {
                result.push_back(sieve[n]);
                n /= sieve[n];
            }
        } else {
            result.push_back(n);
        }

        assert (std::is_sorted(ALL(result)));
        return result;
    }

    std::vector<int64_t> list_all_factors(int64_t n) const {
        auto p = list_prime_factors(n);
        std::vector<int64_t> d;
        d.push_back(1);
        for (int l = 0; l < p.size(); ) {
            int r = l + 1;
            while (r < p.size() and p[r] == p[l]) ++ r;
            int n = d.size();
            REP (k1, r - l) {
                REP (k2, n) {
                    d.push_back(d[d.size() - n] * p[l]);
                }
            }
            l = r;
        }
        return d;
    }

    /**
     * @note O(1) if n < size; O(sqrt n) if size <= n < size^2
     */
    bool is_prime(int64_t n) const {
        assert (1 <= n and n < (int64_t)size * size);
        if (n < size) {
            return sieve[n] == n;
        }
        for (int p : primes) {
            if (n < (int64_t)p * p) {
                break;
            }
            if (n % p == 0) {
                return false;
            }
        }
        return true;
    }
};
#line 3 "number/primes_extra.hpp"
#include <map>
#line 7 "number/primes_extra.hpp"

std::map<int64_t, int> list_prime_factors_as_map(const prepared_primes& primes, int64_t n) {
    std::map<int64_t, int> cnt;
    for (int64_t p : primes.list_prime_factors(n)) {
        ++ cnt[p];
    }
    return cnt;
}

int64_t euler_totient(const prepared_primes& primes, int64_t n) {
    int64_t phi = 1;
    int64_t last = -1;
    for (int64_t p : primes.list_prime_factors(n)) {
        if (last != p) {
            last = p;
            phi *= p - 1;
        } else {
            phi *= p;
        }
    }
    return phi;
}
#line 5 "modulus/choose_simple.hpp"

/**
 * @brief combination / 組合せ ${} _ n C _ r$ (愚直 $O(r)$)
 */
template <int32_t MOD>
mint<MOD> choose_simple(int64_t n, int32_t r) {
    assert (0 <= r and r <= n);
    mint<MOD> num = 1;
    mint<MOD> den = 1;
    REP (i, r) {
        num *= n - i;
        den *= i + 1;
    }
    return num / den;
}
#line 5 "modulus/multichoose_simple.hpp"

/**
 * @brief 重複組合せ ${} _ n H _ r = {} _ {n + r - 1} C _ r$ (愚直 $O(r)$)
 */
template <int32_t MOD>
mint<MOD> multichoose_simple(int64_t n, int32_t r) {
    assert (0 <= n and 0 <= r);
    if (n == 0 and r == 0) return 1;
    return choose_simple<MOD>(n + r - 1, r);
}
#line 8 "number/primes_extra.yukicoder-1659.test.cpp"
using namespace std;

prepared_primes primes(1e6 + 100);

constexpr int64_t MOD = 1000000007;
mint<MOD> solve(int64_t n, int64_t k) {
    mint<MOD> ans = 1;
    for (auto [p, e] : list_prime_factors_as_map(primes, n)) {
        // ans *= multichoose_simple<MOD>(k, e);
        mint<MOD> y = 0;
        REP (x, e + 1) {
            y += multichoose_simple<MOD>(k, x);
        }
        ans *= y;
    }
    return ans;
}

// generated by oj-template v4.8.0 (https://github.com/online-judge-tools/template-generator)
int main() {
    std::ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
    int64_t N, K;
    std::cin >> N >> K;
    auto ans = solve(N, K);
    std::cout << ans << '\n';
    return 0;
}

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