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<algorithm>
#define N 100010
#define mod 1000000007
#define ll long long
using namespace std;
int num[N],tot;
ll n,k,f[N];
ll ksm(ll a,ll b=mod-2)
{
	if(b==0) return 1;
	if(b==1) return a;
	ll q=ksm(a,b>>1);
	if(b&1) return q*q%mod*a%mod;
	return q*q%mod;
}
int main()
{
	scanf("%lld%lld",&n,&k);
	for(int i=1;i*i<=n;i++)
	if(n%i==0)
	{
		num[++tot]=i;
		if(i*i!=n) num[++tot]=n/i;
	}
	sort(num+1,num+tot+1);
	ll ans=0;
	for(int i=1;i<=tot;i++)
	{
		f[i]=ksm(k,(num[i]+1)>>1);
		for(int j=1;j<i;j++)
		if(num[i]%num[j]==0) f[i]=(f[i]-f[j]+mod)%mod;
	}
	for(int i=1;i<=tot;i++)
	ans=(ans+f[i]*num[i]/(num[i]&1?1:2))%mod;
	printf("%lld",ans);
	return 0;
}
