Submission #20111

#TimeUsernameProblemLanguageResultExecution timeMemory
20111gs14004팔찌 (kriii4_V)C++14
6 / 100
1000 ms13440 KiB
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#include <limits.h>
#include <stack>
#include <queue>
#include <map>
#include <set>
#include <algorithm>
#include <string>
#include <functional>
#include <vector>
#include <numeric>
#include <deque>
#include <utility>
#include <bitset>
#include <iostream>
using namespace std;
typedef long long lint;
typedef long double llf;
typedef pair<int, int> pi;
const int mod = 1e9 + 7;

lint ipow(lint x, lint p){
    lint ret = 1, piv = x % mod;
    while(p){
        if(p&1) ret *= piv;
        piv *= piv;
        ret %= mod;
        piv %= mod;
        p >>= 1;
    }
    return ret;
}

int dp[1000005];

int phi(int x){
	if(~dp[x]) return dp[x];
	int tmp = x;
	lint ret = x;
	set<int> s;
	int cnt = 0;
	for(int i=2; i*i<=x; i++){
		if(x % i == 0) s.insert(i);
		while(x % i == 0){
			x /= i;
		}
	}
	if(x > 1) s.insert(x);
	for(auto &i : s){
		ret *= (i-1);
		ret /= i;
	}
	return dp[tmp] = ret;
}

int n, k;
lint kpow[1000005];

int solve(int n, int k){
	lint ret = 0;
	for(int i=1; i*i<=n; i++){
		if(n%i == 0){
			ret += kpow[i] * phi(n/i) % mod;
			if(i*i!=n) ret += kpow[n/i] * phi(i) % mod;
			ret %= mod;
		}
	}
	ret *= ipow(n, mod - 2);
	ret %= mod;
	return ret;
}

int main(){
	memset(dp, -1, sizeof(dp));
	cin >> n >> k;
	kpow[0] = 1;
	for(int i=1; i<=n; i++){
		kpow[i] = kpow[i-1] * k % mod;
	}
	lint ret = 2;
	for(int i=1; i<=n; i++){
		ret += solve(i, k);
		ret %= mod;
		if(i%2 == 0) ret += (1ll * (k+1) * kpow[i/2] % mod) * ((mod + 1) / 2) % mod;
		else ret += kpow[i/2+1];
		ret %= mod;
	}
	ret *= (mod + 1) / 2;
	ret %= mod;
	cout << ret;
}
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