結果
| 問題 | No.1039 Project Euler でやれ |
| ユーザー |
👑  hitonanode
|
| 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 | 24 ms / 2,000 ms |
| コード長 | 11,696 bytes |
| コンパイル時間 | 2,567 ms |
| コンパイル使用メモリ | 215,524 KB |
| 実行使用メモリ | 11,524 KB |
| 最終ジャッジ日時 | 2024-04-25 15:51:09 |
| 合計ジャッジ時間 | 3,701 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge2 |
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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 | 14 ms
8,228 KB |
| testcase_01 | AC | 24 ms
9,760 KB |
| testcase_02 | AC | 19 ms
10,408 KB |
| testcase_03 | AC | 21 ms
11,524 KB |
| testcase_04 | AC | 21 ms
11,432 KB |
| testcase_05 | AC | 20 ms
10,536 KB |
| testcase_06 | AC | 18 ms
9,760 KB |
| testcase_07 | AC | 14 ms
7,712 KB |
| testcase_08 | AC | 14 ms
8,356 KB |
| testcase_09 | AC | 16 ms
9,256 KB |
| testcase_10 | AC | 14 ms
7,804 KB |
| testcase_11 | AC | 19 ms
10,076 KB |
| testcase_12 | AC | 14 ms
8,224 KB |
| testcase_13 | AC | 12 ms
7,704 KB |
| testcase_14 | AC | 16 ms
8,992 KB |
| testcase_15 | AC | 16 ms
9,760 KB |
| testcase_16 | AC | 12 ms
7,616 KB |
| testcase_17 | AC | 11 ms
7,616 KB |
| testcase_18 | AC | 13 ms
7,732 KB |
| testcase_19 | AC | 13 ms
7,576 KB |
ソースコード
#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';
}