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 N 2005
#define LL long long
using namespace std;
const int mo=1e9+7;
int n,k,w[N],lw,f[N],ans;
LL fpm(LL x,LL y){ LL s=1; while(y){ if(y&1) s=(s*x)%mo; y>>=1,x=(x*x)%mo;} return s;}
int main()
{
	int i,j;
	cin>>n>>k;
	for(i=1;i*i<=n;i++)
		if(n%i==0){
			w[++lw]=i;
			if(i*i!=n) w[++lw]=n/i;
		  }
	sort(w+1,w+lw+1);
	for(i=1;i<=lw;i++){
		f[i]=fpm(k,(w[i]+1)/2);
		for(j=1;j<i;j++)
			if(w[i]%w[j]==0)
				f[i]=(f[i]-f[j]+mo)%mo;
		if(w[i]%2==0)
			ans=(ans+1LL*f[i]*(w[i]/2))%mo;
		else
			ans=(ans+1LL*f[i]*w[i])%mo;
	  }
	cout<<ans;
	return 0;
}
