Submission #474613

#	Time	Username	Problem	Language	Result	Execution time	Memory
474613		egod1537	팔찌 (kriii4_V)	C++14	6 / 100	1056 ms	16848 KiB

V

#pragma GCC optimize("O3")
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")

#include<bits/stdc++.h>

using namespace std;

typedef long long ll;
const ll mod = 1e9 + 7;

typedef pair<ll, ll> pi;
#define var first
#define cnt second

ll pwk[2000001];
bitset<1000001> vit;
vector<ll> prime;

ll pow(ll x, ll cnt) {
	if (cnt == 0) return 1;
	ll mid = pow(x, cnt >> 1)%mod;
	return (((mid * mid)%mod) * (cnt % 2 ? x : 1)) % mod;
}
ll revmod(ll x) { return pow(x, mod - 2) % mod; }	
vector<pi> getfactor(ll num) {
	vector<pi> ans;
	for (int i = 0; num > 1 && prime[i]*prime[i] <= num && i < prime.size(); i++) {
		ll now = prime[i];
		pi p = pi(now, 0);
		while (num % now == 0) {
			p.cnt++;
			num /= now;
		}
		if (p.cnt > 0) ans.push_back(p);
	}
	if (num > 1) ans.push_back(pi(num, 1));
	return ans;
}
ll eulerp(vector<pi>& factor, vector<vector<ll>>& psum) {
	ll ans = 1;
	for (int i = 0; i < factor.size(); i++) {
		pi& p = factor[i];
		if (p.cnt == 0) continue;
		ans = (ans * ((psum[i][p.cnt-1] * (p.var - 1)) % mod)) % mod;
	}
	return ans;
}
ll dfs(int num, ll k, ll now, vector<pi>& arr, vector<pi>& dq, vector<vector<ll>>& psum) {
	if (num == arr.size()) return eulerp(dq, psum)*pwk[now];
	ll ans = 0;
	for (int i = 0; i <= arr[num].cnt; i++) {
		dq[num].cnt = arr[num].cnt - i;
		ans = (ans + dfs(num+1, k, now*psum[num][i], arr, dq, psum))%mod;
	}
	return ans;
}
ll r2;
ll func(ll n, ll k) {
	ll ans = 0;
	vector<pi> fact = getfactor(n);
	vector<vector<ll>> psum(fact.size());
	for (int i = 0; i < fact.size(); i++) {
		psum[i].resize(fact[i].cnt+1);
		psum[i][0] = 1;
		for (int j = 1; j <= fact[i].cnt; j++) 
			psum[i][j] = psum[i][j - 1] * fact[i].var;
	}
	vector<pi> dq(fact.begin(), fact.end());
	ans = dfs(0, k, 1, fact, dq, psum);
	if (n % 2) ans = (ans + (n * pwk[n/2+1])%mod)%mod;
	else {
		ll pw = (pwk[n/2] + pwk[n/2+1]) % mod;
		ans = (ans + (((n * pw)%mod)*r2)%mod)%mod;
	}

	return (ans * revmod(2 * n)) % mod;
}

int main() {
	ios::sync_with_stdio(0);
	cin.tie(0), cout.tie(0);

	for (int i = 2; i <= 1000000; i++) {
		if (!vit[i]) prime.push_back(i);
		else continue;
		for (int j = 2 * i; j <= 1000000; j += i) vit[j] = true;
	}

	ll n, k; cin >> n >> k;

	pwk[0] = 1;
	for (int i = 1; i <= 2000000; i++) pwk[i] = (pwk[i - 1] * k) % mod;
	r2 = revmod(2);

	ll ans = 1;
	for (int i = 1; i <= n; i++) ans = (ans + func(i, k)) % mod;
	cout << ans;

	return 0;
}

Compilation message (stderr)

V.cpp: In function 'std::vector<std::pair<long long int, long long int> > getfactor(ll)':
V.cpp:28:59: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<long long int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   28 |  for (int i = 0; num > 1 && prime[i]*prime[i] <= num && i < prime.size(); i++) {
      |                                                         ~~^~~~~~~~~~~~~~
V.cpp: In function 'll eulerp(std::vector<std::pair<long long int, long long int> >&, std::vector<std::vector<long long int> >&)':
V.cpp:42:20: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<std::pair<long long int, long long int> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   42 |  for (int i = 0; i < factor.size(); i++) {
      |                  ~~^~~~~~~~~~~~~~~
V.cpp: In function 'll dfs(int, ll, ll, std::vector<std::pair<long long int, long long int> >&, std::vector<std::pair<long long int, long long int> >&, std::vector<std::vector<long long int> >&)':
V.cpp:50:10: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<std::pair<long long int, long long int> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   50 |  if (num == arr.size()) return eulerp(dq, psum)*pwk[now];
      |      ~~~~^~~~~~~~~~~~~
V.cpp: In function 'll func(ll, ll)':
V.cpp:63:20: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<std::pair<long long int, long long int> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   63 |  for (int i = 0; i < fact.size(); i++) {
      |                  ~~^~~~~~~~~~~~~

• Subtask 1: 6 / 6
• Subtask 2: 0 / 94