Takahashi and Aoki are going to together construct a sequence of integers.

First, Takahashi will provide a sequence of integers a, satisfying all of the following conditions:

* The length of a is N.
* Each element in a is an integer between 1 and K, inclusive.
* a is a palindrome, that is, reversing the order of elements in a will result in the same sequence as the original.



Then, Aoki will perform the following operation an arbitrary number of times:

* Move the first element in a to the end of a.



How many sequences a can be obtained after this procedure, modulo 10^9+7?

Constraints

* 1≤N≤10^9
* 1≤K≤10^9

Input

The input is given from Standard Input in the following format:


N K


Output

Print the number of the sequences a that can be obtained after the procedure, modulo 10^9+7.

Examples

Input

4 2


Output

6


Input

1 10


Output

10


Input

6 3


Output

75


Input

1000000000 1000000000


Output

875699961
#include <bits/stdc++.h>
#define int long long
#define MOD 1000000007
using namespace std;

int power(int x,int y){
	if(!y) return 1;
	int res = power(x * x % MOD,y / 2);
	if(y % 2) res = res * x % MOD;
	return res;
}

signed main(){
	int n,k,ans = 0,cnt[10000] = {};
	vector<int> yaku;
	cin >> n >> k;
	for(int i = 1;i * i <= n;i++){
		if(n % i == 0){
			yaku.push_back(i);
			if(i != n / i) yaku.push_back(n / i);
		}
	}
	sort(yaku.begin(),yaku.end());
	for(int i = 0;i < yaku.size();i++){
		int tmp = power(k,(yaku[i] + 1) / 2);
		for(int j = 0;j < i;j++){
			if(yaku[i] % yaku[j] == 0) tmp = (tmp - cnt[j] + MOD) % MOD;
		}
		cnt[i] = tmp;
		if(yaku[i] % 2) (ans += tmp * yaku[i]) %= MOD;
		else (ans += tmp * yaku[i] / 2) %= MOD;
	}
	cout << ans << endl;
	return 0;
}