結果

問題 No.8123 Calculated N !
ユーザー 👑 獅子座じゃない人
提出日時 2025-04-01 23:12:43
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 1,679 ms / 2,000 ms
コード長 10,894 bytes
コンパイル時間 5,864 ms
コンパイル使用メモリ 333,348 KB
実行使用メモリ 7,328 KB
最終ジャッジ日時 2025-04-01 23:13:13
合計ジャッジ時間 22,703 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge1
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ファイルパターン 結果
sample AC * 6
other AC * 16
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 "yukicoder/play/535/i.cpp"
#ifdef ONLINE_JUDGE
#include <bits/stdc++.h>
#include <atcoder/all>
#else
#include <precompile.h>
#endif

using namespace std;
using ll=long long;
using namespace atcoder;
using mint=modint1000000007;

#define rep1(i, r) for(int i=0; i<(int)(r); ++i)
#define rep2(i, l, r) for(int i=(l); i<(int)(r); ++i)
#define rep3(i, l, r, d) for(int i=(l); i<(int)(r); i+=(d))
#define rep_r1(i, r) for(int i=(r)-1; i>=0; --i)
#define rep_r2(i, l, r) for(int i=(r)-1; i>=(l); --i)
#define rep_r3(i, l, r, d) for(int i=(r)-1; i>=(l); i-=(d))
#define fifth(a, b, c, d, e, ...) e
#define rep(...) fifth(__VA_ARGS__, rep3, rep2, rep1)(__VA_ARGS__)
#define rep_r(...) fifth(__VA_ARGS__, rep_r3, rep_r2, rep_r1)(__VA_ARGS__)

template <typename... T>
void in(T &... args) {
    (cin >> ... >> args);
}
template <typename... T>
void in_z(T &... args) {
    (cin >> ... >> args);
    (..., --args);
}
#define in_d(type, ...) type __VA_ARGS__; in(__VA_ARGS__)
#define in_dz(type, ...) type __VA_ARGS__; in_z(__VA_ARGS__)
template <typename It>
void in_i(It first, It last) {
    for(It it=first;it!=last;++it){
        in(*it);
    }
}
template <typename It>
void in_iz(It first, It last) {
    for(It it=first;it!=last;++it){
        in(*it);
        --*it;
    }
}

template <int N>
struct str_literal {
    static constexpr int length=N-1;
    char buf[N];
    constexpr str_literal(const char (&s_literal)[N]){
        rep(i, N){
            buf[i]=s_literal[i];
        }
        buf[length]='\0';
    }
};
template <int N>
ostream & operator<<(ostream & os, const str_literal<N> & str) {
    os << str.buf;
    return os;
}

template <str_literal tail="\n", bool do_flush=false>
void out() {
    cout << tail;
    if(do_flush){
        cout << flush;
    }
}
template <str_literal split=" ", str_literal tail="\n", bool do_flush=false, typename Hd, typename... Tl>
void out(const Hd & hd, const Tl &... tl) {
    cout << hd;
    if constexpr (sizeof...(Tl)){
        (cout << ... << (cout << split, tl));
    }
    cout << tail;
    if(do_flush){
        cout << flush;
    }
}
template <str_literal split=" ", str_literal tail="\n", bool do_flush=false, typename It>
void out_i(It first, It last) {
    for(It it=first;it!=last;++it){
        if(it!=first){
            cout << split;
        }
        cout << *it;
    }
    cout << tail;
    if(do_flush){
        cout << flush;
    }
}

template <str_literal tail="\n", bool do_flush=false>
void err() {
    cerr << tail;
    if(do_flush){
        cout << flush;
    }
}
template <str_literal split=" ", str_literal tail="\n", bool do_flush=false, typename Hd, typename... Tl>
void err(const Hd & hd, const Tl &... tl) {
    cerr << hd;
    if constexpr (sizeof...(Tl)){
        (cerr << ... << (cerr << split, tl));
    }
    cerr << tail;
    if(do_flush){
        cout << flush;
    }
}
template <str_literal split=" ", str_literal tail="\n", bool do_flush=false, typename It>
void err_i(It first, It last) {
    for(It it=first;it!=last;++it){
        if(it!=first){
            cerr << split;
        }
        cerr << *it;
    }
    cerr << tail;
    if(do_flush){
        cout << flush;
    }
}

#define dir(dx, dy) for(auto [dx, dy]: {pair{1, 0}, {0, 1}, {-1, 0}, {0, -1}})
#define dir_8(dx, dy) for(auto [dx, dy]: {pair{1, 0}, {1, 1}, {0, 1}, {-1, 1}, {-1, 0}, {-1, -1}, {0, -1}, {1, -1}})

#define all(v) (v).begin(), (v).end()
#define all_r(v) (v).rbegin(), (v).rend()

#define dedup(v) (v).erase(unique(all(v)), (v).end())

#define yn(b) ((b) ? "Yes" : "No")

template <typename T1, typename T2>
bool chmin(T1 & l, const T2 & r) {
    if(r<l){
        l=r;
        return true;
    }
    return false;
}
template <typename T1, typename T2>
bool chmax(T1 & l, const T2 & r) {
    if(r>l){
        l=r;
        return true;
    }
    return false;
}

template <typename Hd1, typename Hd2, typename... Tl>
auto min_of(Hd1 hd1, Hd2 hd2, Tl... tl) {
    if constexpr (sizeof...(Tl)==0){
        return min(hd1, hd2);
    } else {
        return min(hd1, min_of(hd2, tl...));
    }
}
template <typename Hd1, typename Hd2, typename... Tl>
auto max_of(Hd1 hd1, Hd2 hd2, Tl... tl) {
    if constexpr (sizeof...(Tl)==0){
        return max(hd1, hd2);
    } else {
        return max(hd1, max_of(hd2, tl...));
    }
}
template <typename Hd1, typename Hd2, typename... Tl>
auto gcd_of(Hd1 hd1, Hd2 hd2, Tl... tl) {
    if constexpr (sizeof...(Tl)==0){
        return gcd(hd1, hd2);
    } else {
        return gcd(hd1, gcd_of(hd2, tl...));
    }
}
template <typename Hd1, typename Hd2, typename... Tl>
auto lcm_of(Hd1 hd1, Hd2 hd2, Tl... tl) {
    if constexpr (sizeof...(Tl)==0){
        return lcm(hd1, hd2);
    } else {
        return lcm(hd1, lcm_of(hd2, tl...));
    }
}

template <typename T, size_t N>
auto make_vector(vector<size_t> & sizes, T const& x) {
    if constexpr (N==1){
        return vector(sizes[0], x);
    } else {
        size_t size=sizes[N-1];
        sizes.pop_back();
        return vector(size, make_vector<T, N-1>(sizes, x));
    }
}
template <typename T, size_t N>
auto make_vector(size_t const(&sizes)[N], T const& x=T()) {
    vector<size_t> s(N);
    rep(i, N){
        s[i] = sizes[N-i-1];
    }
    return make_vector<T, N>(s, x);
}
template <typename T, size_t N>
auto make_vector(vector<int> & sizes, T const& x) {
    if constexpr (N==1){
        return vector(sizes[0], x);
    } else {
        int size=sizes[N-1];
        sizes.pop_back();
        return vector(size, make_vector<T, N-1>(sizes, x));
    }
}
template <typename T, size_t N>
auto make_vector(int const(&sizes)[N], T const& x=T()) {
    vector<int> s(N);
    rep(i, N){
        s[i] = sizes[N-i-1];
    }
    return make_vector<T, N>(s, x);
}
template <typename T, size_t Hd, size_t... Tl>
auto make_array() {
    if constexpr (sizeof...(Tl)==0){
        return array<T, Hd>{};
    } else {
        return array<decltype(make_array<T, Tl...>()), Hd>{};
    }
}

constexpr int inf32=1'000'000'001;
constexpr ll inf64=2'000'000'000'000'000'001;

constexpr ll ten_powers[19]={
    1, 10, 100, 1000, 10000, 100000, 1000000,
    10000000, 100000000, 1000000000, 10000000000,
    100000000000, 1000000000000, 10000000000000,
    100000000000000, 1000000000000000,
    10000000000000000, 100000000000000000,
    1000000000000000000
};

template <typename S, S e>
constexpr S e_const() {
    return e;
}
template <typename S1, S1 e1, typename S2, S2 e2>
constexpr pair<S1, S2> e_pair() {
    return {e1, e2};
}
template <typename S>
S op_min(S a, S b) {
    return min(a, b);
}
template <typename S>
S op_max(S a, S b) {
    return max(a, b);
}
template <typename S>
S op_add(S a, S b) {
    return a+b;
}
template <typename S1, typename S2>
pair<S1, S2> op_add_pair(pair<S1, S2> a, pair<S1, S2> b) {
    auto [a1, a2]=a;
    auto [b1, b2]=b;
    return {a1+b1, a2+b2};
}
template <typename F1, typename F2, typename S>
S mapping_affine(pair<F1, F2> f, S x) {
    auto [a, b]=f;
    return a*x+b;
}
template <typename F1, typename F2, typename S1, typename S2>
pair<S1, S2> mapping_len_and_affine(pair<F1, F2> f, pair<S1, S2> x) {
    auto [a, b]=f;
    auto [x1, x2]=x;
    return {x1, a*x2+b*x1};
}
template <typename F1, typename F2>
pair<F1, F2> composition_affine(pair<F1, F2> f, pair<F1, F2> g) {
    auto [a_f, b_f]=f;
    auto [a_g, b_g]=g;
    return {a_f*a_g, a_f*b_g+b_f};
}

#line 1 "/opt/ei1333_s_library/math/number-theory/prime-table.hpp"
/**
 * @brief Prime Table(素数テーブル)
 *
 */
vector<bool> prime_table(int n) {
  vector<bool> prime(n + 1, true);
  if (n >= 0) prime[0] = false;
  if (n >= 1) prime[1] = false;
  for (int i = 2; i * i <= n; i++) {
    if (!prime[i]) continue;
    for (int j = i * i; j <= n; j += i) {
      prime[j] = false;
    }
  }
  return prime;
}
#line 2 "/opt/ei1333_s_library/math/number-theory/enumerate-primes.hpp"

vector<int> enumerate_primes(int n) {
  if (n <= 1) return {};
  auto d = prime_table(n);
  vector<int> primes;
  primes.reserve(count(begin(d), end(d), true));
  for (int i = 0; i < d.size(); i++) {
    if (d[i]) primes.push_back(i);
  }
  return primes;
}
#line 291 "yukicoder/play/535/i.cpp"

// #include "math/number-theory/prime-count.hpp"
#line 1 "/opt/ei1333_s_library/math/number-theory/kth-root-integer.hpp"
uint64_t kth_root_integer(uint64_t a, int k) {
  if (k == 1) return a;
  auto check = [&](uint32_t x) {
    uint64_t mul = 1;
    for (int j = 0; j < k; j++) {
      if (__builtin_mul_overflow(mul, x, &mul)) return false;
    }
    return mul <= a;
  };
  uint64_t ret = 0;
  for (int i = 31; i >= 0; i--) {
    if (check(ret | (1u << i))) ret |= 1u << i;
  }
  return ret;
}
#line 294 "yukicoder/play/535/i.cpp"

/**
 * @brief Prime Count(素数の個数)
 */
template <int64_t LIM = 100000000000LL>
struct PrimeCount {
 private:
  int64_t sq;
  vector<bool> prime;
  vector<int64_t> prime_sum, primes;

  int64_t p2(int64_t x, int64_t y) {
    if (x < 4) return 0;
    int64_t a = pi(y);
    int64_t b = pi(kth_root_integer(x, 2));
    if (a >= b) return 0;
    int64_t sum = (a - 2) * (a + 1) / 2 - (b - 2) * (b + 1) / 2;
    for (int64_t i = a; i < b; i++) sum += pi(x / primes[i]);
    return sum;
  }

  int64_t phi(int64_t m, int64_t n) {
    if (m < 1) return 0;
    if (n > m) return 1;
    if (n < 1) return m;
    if (m <= primes[n - 1] * primes[n - 1]) return pi(m) - n + 1;
    if (m <= primes[n - 1] * primes[n - 1] * primes[n - 1] && m <= sq) {
      int64_t sx = pi(kth_root_integer(m, 2));
      int64_t ans = pi(m) - (sx + n - 2) * (sx - n + 1) / 2;
      for (int64_t i = n; i < sx; ++i) ans += pi(m / primes[i]);
      return ans;
    }
    return phi(m, n - 1) - phi(m / primes[n - 1], n - 1);
  }

 public:
  PrimeCount() : sq(kth_root_integer(LIM, 2)), prime_sum(sq + 1) {
    prime = prime_table(sq);
    for (int i = 1; i <= sq; i++) prime_sum[i] = prime_sum[i - 1] + prime[i];
    primes.reserve(prime_sum[sq]);
    for (int i = 1; i <= sq; i++)
      if (prime[i]) primes.push_back(i);
  }

  int64_t pi(int64_t n) {
    if (n <= sq) return prime_sum[n];
    int64_t m = kth_root_integer(n, 3);
    int64_t a = pi(m);
    return phi(n, a) + a - 1 - p2(n, m);
  }
};


uint64_t uint64_floor_sqrt(uint64_t n) {
    if (n == 0) return 0; 
    uint64_t tmp_m1 = std::sqrt(n) - 1;
    return tmp_m1 * (tmp_m1 + 2) < n ? tmp_m1 + 1 : tmp_m1;
}

int main(void) {
    cout << fixed << setprecision(15);
    cerr << fixed << setprecision(15);
    in_d(ll, n);
    ll sqrt_n=uint64_floor_sqrt(n);
    auto primes=enumerate_primes(sqrt_n);
    mint ans=1;
    for(auto p: primes){
        mint b=1;
        ll p_pow=p;
        while(p_pow<=n){
            b+=n/p_pow;
            p_pow*=p;
        }
        ans*=b;
    }
    PrimeCount<> pc;
    for(ll q=1;q<=sqrt_n;++q){
        ll r=n/q;
        ll l=n/(q+1);
        ans*=mint(q+1).pow(pc.pi(r)-pc.pi(max(l, sqrt_n)));
    }
    out(ans.val());
    return 0;
}
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