Submission #474619

#	Time	Username	Problem	Language	Result	Execution time	Memory
474619		egod1537	팔찌 (kriii4_V)	C++14	6 / 100	1012 ms	29760 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], phi[1000001], low[1000001];
bitset<1000001> vit;
vector<ll> prime;

ll pow(ll x, ll p) {
	ll ret = 1, piv = x % mod;
	while (p) {
		if (p & 1) ret *= piv;
		piv *= piv;
		ret %= mod;
		piv %= mod;
		p >>= 1;
	}
	return ret;
}
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 dfs(int num, ll k, ll now, ll np, vector<pi>& arr, vector<vector<ll>>& psum) {
	if (num == arr.size()) return phi[np]*pwk[now];
	ll ans = 0;
	for (int i = 0; i <= arr[num].cnt; i++) 
		ans = (ans + dfs(num+1, k, now*psum[num][i], np*psum[num][arr[num].cnt-i], arr, psum))%mod;
	return ans;
}
ll r2;
ll func(ll n, ll k) {
	//if (n % 10000 == 0) cout << n << "\n";
	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;
	}
	ans = dfs(0, k, 1, 1, fact, 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;

	phi[1] = 1;
	for (int i = 2; i <= n; i++) {
		for (int j = i; j <= n; j += i) {
			if (!low[j]) low[j] = i;
		}
		phi[i] = i;
		for (int j = i; j != 1; ) {
			int p = low[j];
			while (j % p == 0) {
				j /= p;
			}
			phi[i] = (1ll * phi[i] * (p - 1)) / p;
		}
	}

	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:34:59: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<long long int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   34 |  for (int i = 0; num > 1 && prime[i]*prime[i] <= num && i < prime.size(); i++) {
      |                                                         ~~^~~~~~~~~~~~~~
V.cpp: In function 'll dfs(int, ll, ll, ll, std::vector<std::pair<long long int, long long int> >&, std::vector<std::vector<long long int> >&)':
V.cpp:47:10: 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]
   47 |  if (num == arr.size()) return phi[np]*pwk[now];
      |      ~~~~^~~~~~~~~~~~~
V.cpp: In function 'll func(ll, ll)':
V.cpp:59:20: 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]
   59 |  for (int i = 0; i < fact.size(); i++) {
      |                  ~~^~~~~~~~~~~~~

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