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 mo=int(1e9+7);
int n,k,m,a[2000],f[2000],ans;

int qpow(int a,int b)
{
	int x=a;  a=1;
	while (b)
		{
			if (b&1)  a=1LL*a*x%mo;
			x=1LL*x*x%mo,b>>=1;
		}
	return a;
}

void work()
{
	scanf("%d %d",&n,&k);
	for (int i=1; i*i<=n; i++)
		if (n%i==0)
			{
				a[++m]=i;
				if (i!=n/i)  a[++m]=n/i;
			}
	sort(a+1,a+m+1);
	for (int i=1; i<=m; i++)
		f[i]=qpow(k,(a[i]+1)/2);
	for (int i=1; i<=m; i++)
		for (int j=i+1; j<=m; j++)
			if (a[j]%a[i]==0)
				f[j]=(f[j]+mo-f[i])%mo;
	for (int i=1; i<=m; i++)
		if (a[i]&1)  ans=(ans+1LL*f[i]*a[i])%mo;
		else  ans=(ans+1LL*f[i]*a[i]/2)%mo;
	printf("%d",ans);
}

int main()
{
	work();
	return 0;
}
