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>
using namespace std;
const int md=1e9+7;
int n,m,cc,a[10005],dp[10005],ans;
int pw(int x,int b){int res=1;for(;b;b>>=1,x=1ll*x*x%md)if(b&1)res=1ll*res*x%md;return res;}
int main()
{
	scanf("%d%d",&n,&m);
	for(int i=1;i*i<=n;i++)if(n%i==0)
	{
		a[++cc]=i;
		if(i*i!=n)a[++cc]=n/i;
	}
	sort(a+1,a+cc+1);
	for(int i=1;i<=cc;i++)
	{
		dp[i]=pw(m,(a[i]+1)/2);
		for(int j=1;j<i;j++)if(a[i]%a[j]==0)dp[i]=(dp[i]-dp[j]+md)%md;
		if(a[i]&1)ans=(ans+1ll*dp[i]*a[i]%md)%md;else ans=(ans+1ll*dp[i]*(a[i]/2)%md)%md;
	}
	printf("%d\n",ans);
}