結果

問題 No.1164 GCD Products hard
ユーザー hitonanodehitonanode
提出日時 2020-08-11 23:48:48
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 1,347 ms / 2,500 ms
コード長 10,171 bytes
コンパイル時間 2,050 ms
コンパイル使用メモリ 202,136 KB
実行使用メモリ 81,384 KB
最終ジャッジ日時 2024-04-17 17:53:39
合計ジャッジ時間 20,320 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge3
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 861 ms
56,896 KB
testcase_01 AC 978 ms
62,848 KB
testcase_02 AC 648 ms
47,336 KB
testcase_03 AC 191 ms
18,180 KB
testcase_04 AC 123 ms
19,108 KB
testcase_05 AC 866 ms
56,064 KB
testcase_06 AC 928 ms
67,200 KB
testcase_07 AC 933 ms
70,556 KB
testcase_08 AC 890 ms
70,292 KB
testcase_09 AC 655 ms
49,388 KB
testcase_10 AC 173 ms
16,640 KB
testcase_11 AC 676 ms
52,484 KB
testcase_12 AC 1,031 ms
66,556 KB
testcase_13 AC 565 ms
41,280 KB
testcase_14 AC 428 ms
48,896 KB
testcase_15 AC 944 ms
71,736 KB
testcase_16 AC 510 ms
52,992 KB
testcase_17 AC 830 ms
54,528 KB
testcase_18 AC 751 ms
50,048 KB
testcase_19 AC 129 ms
20,244 KB
testcase_20 AC 312 ms
28,364 KB
testcase_21 AC 1,169 ms
71,804 KB
testcase_22 AC 2 ms
5,376 KB
testcase_23 AC 709 ms
81,184 KB
testcase_24 AC 1,347 ms
81,384 KB
testcase_25 AC 2 ms
5,376 KB
testcase_26 AC 2 ms
5,376 KB
testcase_27 AC 2 ms
5,376 KB
testcase_28 AC 2 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 <bits/stdc++.h>
using namespace std;
using lint = long long;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios { fast_ios(){ cin.tie(nullptr); 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 V, typename T> void ndfill(V &x, const T &val) { x = val; }
template <typename V, typename T> void ndfill(vector<V> &vec, const T &val) { for (auto &v : vec) ndfill(v, val); }
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> vector<T> srtunq(vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }
template <typename T> istream &operator>>(istream &is, vector<T> &vec) { for (auto &v : vec) is >> v; return is; }
template <typename... T> istream &operator>>(istream &is, tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); 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 tuple<T...> &tpl) { std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); 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; }
#ifdef HITONANODE_LOCAL
#define dbg(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ") " << __FILE__ << endl
#else
#define dbg(x)
#endif

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>;
using mint2 = ModInt<1000000006>;

#include <vector>

// f[n]のn >= 1に対して、全ての倍数n*iに対するf[n*i]の和が出てくる 計算量O(NlogN)
template <typename T>
void integer_zeta(std::vector<T> &f)
{
    int N = f.size() - 1;
    for (int i = 1; i <= N; i++) {
        for (int j = i * 2; j <= N; j += i) {
            f[i] += f[j];
        }
    }
}

// f[n]に対して、全てのnの倍数n*iに対するf[n*i]の和が出てくる 計算量O(NloglogN)
// 素数p毎に処理する高速ゼータ変換
// 使用例 <https://yukicoder.me/submissions/385043>
template <typename T>
void fast_integer_zeta(std::vector<T> &f)
{
    int N = f.size() - 1;
    std::vector<int> is_prime(N + 1, 1);
    for (int p = 2; p <= N; p++) if (is_prime[p]) {
        for (int q = p * 2; q <= N; q += p) is_prime[q] = 0;
        for (int j = N / p * p; j > 0; j -= p) f[j / p] += f[j];
    }
}

// fast_integer_zetaの逆演算 O(NloglogN)
// 使用例 <https://yukicoder.me/submissions/385120>
template <typename T>
void fast_integer_moebius(std::vector<T> &f)
{
    int N = f.size() - 1;
    std::vector<int> is_prime(N + 1, 1);
    for (int p = 2; p <= N; p++) if (is_prime[p]) {
        for (int q = p * 2; q <= N; q += p) is_prime[q] = 0;
        for (int j = p; j <= N; j += p) f[j / p] -= f[j];
    }
}

int main()
{
    int A, B, N;
    cin >> A >> B >> N;
    vector<mint2> cnt(B + 1);
    vector<mint2> pown(1001);
    REP(i, pown.size()) pown[i] = mint2(i).power(N);
    FOR(x, 1, B + 1)
    {
        int n = B / x - (A - 1) / x;
        if (n)
        {
            cnt[x] = (n < pown.size() ? pown[n] : mint2(n).power(N));
        }
    }
    dbg(cnt);
    fast_integer_moebius(cnt);
    mint ret = 1;
    FOR(x, 1, B + 1) ret *= mint(x).power(cnt[x].val);
    cout << ret << '\n';
}
0