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<algorithm>
#include<cmath>
#define fo(i,a,b) for(i=a;i<=b;i++)
using namespace std;
typedef long long ll;
const int mo=1000000007,inv2=(mo+1)/2;
int d[3000],f[3000];
int i,j,k,l,t,n,m,top,ans;
int qsm(int x,int y){
	if (!y) return 1;
	int t=qsm(x,y/2);
	t=(ll)t*t%mo;
	if (y%2) t=(ll)t*x%mo;
	return t;
}
int main(){
	scanf("%d%d",&n,&k);
	t=floor(sqrt(n));
	fo(i,1,t)
		if (n%i==0){
			d[++top]=i;
			if (i!=n/i) d[++top]=n/i;
		}
	sort(d+1,d+top+1);
	fo(i,1,top){
		f[i]=qsm(k,(d[i]+1)/2);
		fo(j,1,i-1)
			if (d[i]%d[j]==0) (f[i]-=f[j])%=mo;
		if (d[i]%2==0) (ans+=(ll)f[i]*d[i]%mo*inv2%mo)%=mo;
		else (ans+=(ll)f[i]*d[i]%mo)%=mo;
	}
	(ans+=mo)%=mo;
	printf("%d\n",ans);
}