結果

問題 No.1039 Project Euler でやれ
ユーザー hitonanodehitonanode
提出日時 2020-04-24 23:00:42
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 26 ms / 2,000 ms
コード長 11,696 bytes
コンパイル時間 2,647 ms
コンパイル使用メモリ 221,876 KB
実行使用メモリ 11,432 KB
最終ジャッジ日時 2024-11-08 02:58:24
合計ジャッジ時間 3,780 ms
ジャッジサーバーID
（参考情報） 		judge5 / 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 17 ms
8,228 KB
testcase_01 AC 26 ms
9,636 KB
testcase_02 AC 22 ms
10,276 KB
testcase_03 AC 25 ms
11,300 KB
testcase_04 AC 24 ms
11,432 KB
testcase_05 AC 22 ms
10,656 KB
testcase_06 AC 20 ms
9,892 KB
testcase_07 AC 15 ms
7,716 KB
testcase_08 AC 17 ms
8,352 KB
testcase_09 AC 19 ms
9,124 KB
testcase_10 AC 16 ms
7,716 KB
testcase_11 AC 21 ms
10,016 KB
testcase_12 AC 16 ms
7,972 KB
testcase_13 AC 15 ms
7,680 KB
testcase_14 AC 19 ms
8,996 KB
testcase_15 AC 20 ms
9,632 KB
testcase_16 AC 14 ms
7,680 KB
testcase_17 AC 15 ms
7,680 KB
testcase_18 AC 14 ms
7,808 KB
testcase_19 AC 14 ms
7,808 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 <bits/stdc++.h>
using namespace std;
using lint = long long int;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios { fast_ios(){ cin.tie(0); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_;
#define ALL(x) (x).begin(), (x).end()
#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)
#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
template<typename T> void ndarray(vector<T> &vec, int len) { vec.resize(len); }
template<typename T, typename... Args> void ndarray(vector<T> &vec, int len, Args... args) { vec.resize(len); for (auto &v : vec) ndarray(v, args...); }
template<typename T> bool chmax(T &m, const T q) { if (m < q) {m = q; return true;} else return false; }
template<typename T> bool chmin(T &m, const T q) { if (m > q) {m = q; return true;} else return false; }
template<typename T1, typename T2> pair<T1, T2> operator+(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first + r.first, l.second + r.second); }
template<typename T1, typename T2> pair<T1, T2> operator-(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first - r.first, l.second - r.second); }
template<typename T> istream &operator>>(istream &is, vector<T> &vec){ for (auto &v : vec) is >> v; return is; }
template<typename T> ostream &operator<<(ostream &os, const vector<T> &vec){ os << "["; for (auto v : vec) os << v << ","; os << "]"; return os; }
template<typename T> ostream &operator<<(ostream &os, const deque<T> &vec){ os << "deq["; for (auto v : vec) os << v << ","; os << "]"; return os; }
template<typename T> ostream &operator<<(ostream &os, const set<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template<typename T> ostream &operator<<(ostream &os, const unordered_set<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template<typename T> ostream &operator<<(ostream &os, const multiset<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template<typename T> ostream &operator<<(ostream &os, const unordered_multiset<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template<typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &pa){ os << "(" << pa.first << "," << pa.second << ")"; return os; }
template<typename TK, typename TV> ostream &operator<<(ostream &os, const map<TK, TV> &mp){ os << "{"; for (auto v : mp) os << v.first << "=>" << v.second << ","; os << "}"; return os; }
template<typename TK, typename TV> ostream &operator<<(ostream &os, const unordered_map<TK, TV> &mp){ os << "{"; for (auto v : mp) os << v.first << "=>" << v.second << ","; os << "}"; return os; }
#define dbg(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ") " << __FILE__ << endl;
/*
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/tag_and_trait.hpp>
using namespace __gnu_pbds; // find_by_order(), order_of_key()
template<typename TK> using pbds_set = tree<TK, null_type, less<TK>, rb_tree_tag, tree_order_statistics_node_update>;
template<typename TK, typename TV> using pbds_map = tree<TK, TV, less<TK>, rb_tree_tag, tree_order_statistics_node_update>;
*/

template <int mod>
struct ModInt
{
    using lint = long long;
    static int get_mod() { return mod; }
    static int get_primitive_root() {
        static int primitive_root = 0;
        if (!primitive_root) {
            primitive_root = [&](){
                std::set<int> fac;
                int v = mod - 1;
                for (lint i = 2; i * i <= v; i++) while (v % i == 0) fac.insert(i), v /= i;
                if (v > 1) fac.insert(v);
                for (int g = 1; g < mod; g++) {
                    bool ok = true;
                    for (auto i : fac) if (ModInt(g).power((mod - 1) / i) == 1) { ok = false; break; }
                    if (ok) return g;
                }
                return -1;
            }();
        }
        return primitive_root;
    }
    int val;
    constexpr ModInt() : val(0) {}
    constexpr ModInt &_setval(lint v) { val = (v >= mod ? v - mod : v); return *this; }
    constexpr ModInt(lint v) { _setval(v % mod + mod); }
    explicit operator bool() const { return val != 0; }
    constexpr ModInt operator+(const ModInt &x) const { return ModInt()._setval((lint)val + x.val); }
    constexpr ModInt operator-(const ModInt &x) const { return ModInt()._setval((lint)val - x.val + mod); }
    constexpr ModInt operator*(const ModInt &x) const { return ModInt()._setval((lint)val * x.val % mod); }
    constexpr ModInt operator/(const ModInt &x) const { return ModInt()._setval((lint)val * x.inv() % mod); }
    constexpr ModInt operator-() const { return ModInt()._setval(mod - val); }
    constexpr ModInt &operator+=(const ModInt &x) { return *this = *this + x; }
    constexpr ModInt &operator-=(const ModInt &x) { return *this = *this - x; }
    constexpr ModInt &operator*=(const ModInt &x) { return *this = *this * x; }
    constexpr ModInt &operator/=(const ModInt &x) { return *this = *this / x; }
    friend constexpr ModInt operator+(lint a, const ModInt &x) { return ModInt()._setval(a % mod + x.val); }
    friend constexpr ModInt operator-(lint a, const ModInt &x) { return ModInt()._setval(a % mod - x.val + mod); }
    friend constexpr ModInt operator*(lint a, const ModInt &x) { return ModInt()._setval(a % mod * x.val % mod); }
    friend constexpr ModInt operator/(lint a, const ModInt &x) { return ModInt()._setval(a % mod * x.inv() % mod); }
    constexpr bool operator==(const ModInt &x) const { return val == x.val; }
    constexpr bool operator!=(const ModInt &x) const { return val != x.val; }
    bool operator<(const ModInt &x) const { return val < x.val; }  // To use std::map<ModInt, T>
    friend std::istream &operator>>(std::istream &is, ModInt &x) { lint t; is >> t; x = ModInt(t); return is; }
    friend std::ostream &operator<<(std::ostream &os, const ModInt &x) { os << x.val;  return os; }
    constexpr lint power(lint n) const {
        lint ans = 1, tmp = this->val;
        while (n) {
            if (n & 1) ans = ans * tmp % mod;
            tmp = tmp * tmp % mod;
            n /= 2;
        }
        return ans;
    }
    constexpr lint inv() const { return this->power(mod - 2); }
    constexpr ModInt operator^(lint n) const { return ModInt(this->power(n)); }
    constexpr ModInt &operator^=(lint n) { return *this = *this ^ n; }

    inline ModInt fac() const {
        static std::vector<ModInt> facs;
        int l0 = facs.size();
        if (l0 > this->val) return facs[this->val];

        facs.resize(this->val + 1);
        for (int i = l0; i <= this->val; i++) facs[i] = (i == 0 ? ModInt(1) : facs[i - 1] * ModInt(i));
        return facs[this->val];
    }

    ModInt doublefac() const {
        lint k = (this->val + 1) / 2;
        if (this->val & 1) return ModInt(k * 2).fac() / ModInt(2).power(k) / ModInt(k).fac();
        else return ModInt(k).fac() * ModInt(2).power(k);
    }

    ModInt nCr(const ModInt &r) const {
        if (this->val < r.val) return ModInt(0);
        return this->fac() / ((*this - r).fac() * r.fac());
    }

    ModInt sqrt() const {
        if (val == 0) return 0;
        if (mod == 2) return val;
        if (power((mod - 1) / 2) != 1) return 0;
        ModInt b = 1;
        while (b.power((mod - 1) / 2) == 1) b += 1;
        int e = 0, m = mod - 1;
        while (m % 2 == 0) m >>= 1, e++;
        ModInt x = power((m - 1) / 2), y = (*this) * x * x;
        x *= (*this);
        ModInt z = b.power(m);
        while (y != 1) {
            int j = 0;
            ModInt t = y;
            while (t != 1) j++, t *= t;
            z = z.power(1LL << (e - j - 1));
            x *= z, z *= z, y *= z;
            e = j;
        }
        return ModInt(std::min(x.val, mod - x.val));
    }
};
using mint = ModInt<1000000007>;

// Sieve of Eratosthenes
// (*this)[i] = (divisor of i, greater than 1)
// Example: [0, 1, 2, 3, 2, 5, 3, 7, 2, 3, 2, 11, ...]
// Complexity: Space O(MAXN), Time (construction) O(MAXNloglogMAXN)
struct SieveOfEratosthenes : std::vector<int>
{
    std::vector<int> primes;
    SieveOfEratosthenes(int MAXN) : std::vector<int>(MAXN + 1) {
        std::iota(begin(), end(), 0);
        for (int i = 2; i <= MAXN; i++) {
            if ((*this)[i] == i) {
                primes.push_back(i);
                for (int j = i; j <= MAXN; j += i) (*this)[j] = i;
            }
        }
    }
    using T = long long int;
    // Prime factorization for x <= MAXN^2
    // Complexity: O(log x)          (x <= MAXN)
    //             O(MAXN / logMAXN) (MAXN < x <= MAXN^2)
    std::map<T, int> Factorize(T x) {
        assert(x <= 1LL * (int(size()) - 1) * (int(size()) - 1));
        std::map<T, int> ret;
        if (x < int(size())) {
            while (x > 1) {
                ret[(*this)[x]]++;
                x /= (*this)[x];
            }
        }
        else {
            for (auto p : primes) {
                while (!(x % p)) x /= p, ret[p]++;
                if (x == 1) break;
            }
            if (x > 1) ret[x]++;
        }
        return ret;
    }
    std::vector<T> Divisors(T x) {
        std::vector<T> ret{1};
        for (auto p : Factorize(x)) {
            int n = ret.size();
            for (int i = 0; i < n; i++) {
                for (T a = 1, d = 1; d <= p.second; d++) {
                    a *= p.first;
                    ret.push_back(ret[i] * a);
                }
            }
        }
        return ret; // Not sorted
    }
    // Moebius function Table
    // return: [0=>0, 1=>1, 2=>-1, 3=>-1, 4=>0, 5=>-1, 6=>1, 7=>-1, 8=>0, ...]
    std::vector<int> GenerateMoebiusFunctionTable() {
        std::vector<int> ret(size());
        for (int i = 1; i < int(size()); i++) {
            if (i == 1) ret[i] = 1;
            else if ((i / (*this)[i]) % (*this)[i] == 0) ret[i] = 0;
            else ret[i] = -ret[i / (*this)[i]];
        }
        return ret;
    }
};
SieveOfEratosthenes sieve(1000000);

mint solve(int p, int esum)
{
    mint ret = 0;
    vector<mint> ppow(1000, 1);
    REP(i, ppow.size() - 1) ppow[i + 1] = ppow[i] * p;

    vector<int> es, C, D;
    REP(S, 1 << (esum - 1))
    {
        es.clear();
        int last = -1;
        bool ok = true;
        REP(i, esum - 1) if ((S >> i) & 1)
        {
            es.emplace_back(i - last);
            if (es.size() > 1 and es[es.size() - 2] > es[es.size() - 1])
            {
                ok = false;
                break;
            }
            last = i;
        }
        es.emplace_back(esum - 1 - last);
        if (es.size() > 1 and es[es.size() - 2] > es[es.size() - 1])
        {
            ok = false;
        }
        if (!ok) continue;
        C = es, D = es;
        REP(i, es.size()) C[i] = D[i] = i + 1;
        REP(i, es.size() - 1) if (es[i] == es[i + 1]) chmin(C[i + 1], C[i]);
        IREP(i, es.size() - 1) if (es[i] == es[i + 1]) chmax(D[i], D[i + 1]);
        mint tmp = 1;
        int n = es.size();
        REP(k, n) tmp *= (ppow[D[k]] - ppow[k]) * ppow[es[k] * (n - D[k])] * ppow[(es[k] - 1) * (n - C[k] + 1)];
        ret += 1 / tmp;
    }
    return ret;
}
int main()
{
    int M;
    cin >> M;
    if (M == 1)
    {
        puts("1");
        return 0;
    }
    auto facs = sieve.Factorize(M);
    int esum = 0;
    for (auto p : facs) esum = gcd(esum, p.second);
    mint ret = 1;
    for (auto pa : facs)
    {
        ret *= solve(pa.first, pa.second);
    }

    cout << ret * mint(M).fac() << '\n';
}
0