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>
int n,k,cnt,a[10000],b[10000],ans;
const int mu=1000000007;
int ksm(int x,int y){
	int ans=1;
	for (;y;y>>=1,x=x*1ll*x%mu)
		if (y&1) ans=ans*1ll*x%mu;
	return ans;
}
int main(){
	scanf("%d%d",&n,&k);
	int x=(int)sqrt(n);
	for (int i=1;i<=x;i++) 
		if (n%i==0) a[++cnt]=i;
	int t=cnt;
	if (a[cnt]*a[cnt]==n) t--;
	for (int i=t;i>=1;i--) a[++cnt]=n/a[i];
	for (int i=1;i<=cnt;i++){
		b[i]=ksm(k,(a[i]+1)/2);
		for (int j=1;j<i;j++) 
			if (a[i]%a[j]==0) b[i]=(b[i]-b[j])%mu;
		b[i]=(b[i]+mu)%mu;
		if (a[i]%2==0) ans=(ans+a[i]/2*1ll*b[i])%mu;
		else ans=(ans+a[i]*1ll*b[i])%mu;
	}
	printf("%d\n",ans);
}