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;
const int mod=1000000007;
int fpow(int x,int y)
{
	if(y==0)
		return 1;
	int ret=fpow(x,y>>1);
	ret=(long long)ret*ret%mod;
	if(y&1)
		ret=(long long)ret*x%mod;
	return ret;
}
int q[10101],qn;
int f[10101];
int main()
{
	int n,k;
	int ans=0;
	scanf("%d%d",&n,&k);
	qn=0;
	for(int i=1;i*i<=n;i++)
		if(n%i==0)
		{
			q[++qn]=i;
			if(i*i!=n)
				q[++qn]=n/i;
		}
	sort(q+1,q+1+qn);
	for(int i=1;i<=qn;i++)
	{
		f[i]=fpow(k,(q[i]+1)>>1);
		for(int j=1;j<i;j++)
			if(q[i]%q[j]==0)
				(f[i]+=mod-f[j])%=mod;
	}
	for(int i=1;i<=qn;i++)
		if(q[i]&1)
			ans=((long long)f[i]*q[i]+ans)%mod;
		else
			ans=((long long)f[i]*q[i]/2+ans)%mod;
	printf("%d",ans);
	return 0;
}