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<iostream>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<algorithm>
using namespace std;

typedef long long LL;

const int N=3005;
const int MOD=1000000007;

int n,k,tot,a[N],f[N];

int ksm(int x,int y)
{
	int ans=1;
	while (y)
	{
		if (y&1) ans=(LL)ans*x%MOD;
		x=(LL)x*x%MOD;y>>=1;
	}
	return ans;
}

int main()
{
	scanf("%d%d",&n,&k);
	for (int i=1;i*i<=n;i++)
		if (n%i==0)
		{
			a[++tot]=i;
			if (i*i<n) a[++tot]=n/i;
		}
	sort(a+1,a+tot+1);
	int ny2=ksm(2,MOD-2),ans=0;
	for (int i=1;i<=tot;i++)
	{
		f[i]=ksm(k,(a[i]+1)/2);
		for (int j=1;j<i;j++)
			if (a[i]%a[j]==0) (f[i]+=MOD-f[j])%=MOD;
		if (a[i]&1) (ans+=(LL)f[i]*a[i]%MOD)%=MOD;
		else (ans+=(LL)f[i]*a[i]%MOD*ny2%MOD)%=MOD;
	}
	printf("%d",ans);
	return 0;
}