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>
const int mo=1e9+7;
int n,k,a[2000],xb,f[2000],i,j,l,ans;
inline int poww(int x,int y){int ans=1;for(;y;y>>=1,x=1ll*x*x%mo)if(y&1)ans=1ll*ans*x%mo;return ans;}
int main(){
	scanf("%d%d",&n,&k);
	for(i=1;i*i<=n;++i)if(n%i==0){a[++xb]=i;if(i*i<n)a[++xb]=n/i;}
	std::sort(a+1,a+xb+1);
	for(j=1;j<=xb;ans=(ans+1ll*f[j]*(a[j]&1?a[j]:a[j]/2))%mo,++j)
		for(f[j]=poww(k,a[j]+1>>1),l=1;l<j;++l)if(a[j]%a[l]==0)f[j]=(f[j]+mo-f[l])%mo;
	printf("%d\n",ans);
	return 0;
}