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>
#define mod 1000000007
using namespace std;
int n,k,a[2000],dp[2000],tp;
int qpow(int a,int b){
	int ans=1,tmp=a;
	for(;b;b>>=1,tmp=1ll*tmp*tmp%mod)
		if(b&1)ans=1ll*ans*tmp%mod;
	return ans;
}
int main(){
	scanf("%d%d",&n,&k);
	for(int i=1;i*i<=n;i++)if(n%i==0){
		a[++tp]=i;
		if(i*i!=n)a[++tp]=n/i;
	}
	sort(a+1,a+tp+1);
	for(int i=1;i<=tp;++i){
		dp[i]=qpow(k,(a[i]+1)/2);
		for(int j=1;j<i;++j)if(a[i]%a[j]==0)
			dp[i]=(dp[i]-dp[j]+mod)%mod;
	}
	int ans=0;
	for(int i=1;i<=tp;++i)
		ans=(ans+1ll*(a[i]&1?a[i]:a[i]/2)*dp[i])%mod;
	printf("%d",ans);
}