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 <cstdio>
#include <cstdlib>
#include <iostream>
#include <cmath>
#include <cstring>
#include <algorithm>
#define fo(i,a,b) for(int i=a;i<=b;++i)
#define fod(i,a,b) for(int i=a;i>=b;--i)
#define mo 1000000007
#define LL long long
using namespace std;
LL ksm(LL k,LL n)
{
	LL s=1;
	for(;n;n>>=1,k=k*k%mo) if(n&1) s=s*k%mo;
	return s;
}
int pi[100005];
LL f[100005];
int main()
{
	LL n,m;
	cin>>n>>m;
	fo(i,1,sqrt(n)) 
	{
		if(n%i==0) 
		{
			pi[++pi[0]]=i;
			if(n%(n/i)==0&&n/i!=i) pi[++pi[0]]=n/i;
		}
	}
	LL ans=0;
	sort(pi+1,pi+pi[0]+1);
	fo(i,1,pi[0])
	{
		if(n/pi[i]%2==0)
		{
			f[i]=ksm(m,pi[i]);
		}
		else
		{
			f[i]=ksm(m,(pi[i]+1)/2);
		}
		fo(j,1,i-1) if(pi[i]%pi[j]==0) f[i]=(f[i]-f[j]+mo)%mo;
		ans=(ans+f[i]*pi[i])%mo;
	}
	printf("%lld\n",ans);
}