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>
using namespace std;
const int N=2005,Mod=1e9+7;
int v[N],f[N];
inline int qpow(int a,int b){
	int ans=1;
	while (b){
		if (b&1) ans=1ll*ans*a%Mod;
		a=1ll*a*a%Mod,b>>=1;
	}
	return ans;
}
int main(){
    int n,k,tot=0,ans=0;
    scanf ("%d%d",&n,&k);
    for (int i=1; i*i<=n; i++)
        if (n%i==0) {
			v[++tot]=i;
			if (i*i!=n) v[++tot]=n/i;
		}
    sort(v+1,v+tot+1);
    for (int i=1; i<=tot; i++){
        f[i]=qpow(k,(v[i]+1)/2);
        for (int j=1; j<i; j++) if (v[i]%v[j]==0) f[i]=(f[i]-f[j]+Mod)%Mod;
        if (v[i]&1) ans=(1ll*ans+1ll*v[i]*f[i]%Mod)%Mod;
        else ans=(1ll*ans+1ll*(v[i]/2)*f[i]%Mod)%Mod;
    }
    printf ("%d",ans);
    return 0;
}