Submission #20113

#TimeUsernameProblemLanguageResultExecution timeMemory
20113gs14004팔찌 (kriii4_V)C++14
100 / 100
567 ms25160 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 low[1000005], phi[1000005];
lint kpow[1000005], inv[1000005];
int n, k;

int main(){
	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;
		}
	}
	kpow[0] = 1;
	for(int i=1; i<=n; i++){
		kpow[i] = kpow[i-1] * k % mod;
		inv[i] = ipow(i, mod-2);
	}
	lint ret = 2;
	for(int i=1; i<=n; i++){
		for(int j=i; j<=n; j+=i){
			lint tmp = kpow[i] * phi[j/i] % mod;
			tmp *= inv[j];
			tmp %= mod;
			ret += tmp;
		}
	}
	for(int i=1; i<=n; i++){
		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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