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 <cstdio>

const int mo=1000000007;
int a[2000],f[2000];

int ksm(int x,int y){
	int i=1;
	for (;y;y>>=1,x=1ll*x*x%mo)
		if (y&1) i=1ll*i*x%mo;
	return i;
}

int main(){
	int n,k,m=0,ans=0;
	scanf("%d%d\n",&n,&k);
	for (int i=1;i*i<=n;i++)
		if (n%i==0) a[++m]=i;
	for (int i=m;i;i--)
		if (a[i]*a[i]!=n) a[++m]=n/a[i];
	for (int i=1;i<=m;i++){
		f[i]=ksm(k,(a[i]+1)/2);
		for (int j=1;j<i;j++)
			if (a[i]%a[j]==0) (f[i]-=f[j])%=mo;
		ans=(ans+1ll*f[i]*(a[i]&1?a[i]:a[i]/2))%mo;
	}
	printf("%d\n",(ans+mo)%mo);
}