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 <algorithm>
#include <cstring>
#include <cmath>
using namespace std;
const int N=2010,Mo=1000000007;
int v[N],f[N];
inline int Pow(int x,int y) {
    int ret=1;
    while(y) {
	if(y&1) ret=1LL*ret*x%Mo;
	x=1LL*x*x%Mo,y>>=1;
    }
    return ret;
}
int main() {
    int n,k,tp=0,ans=0;
    cin>>n>>k;
    for(int i=1;i*i<=n;i++)
	if(n%i==0) {
	    v[++tp]=i;
	    if(i*i!=n) v[++tp]=n/i;
	}
    sort(v+1,v+1+tp);
    for(int i=1;i<=tp;i++) {
	int x=v[i];
	f[i]=Pow(k,(x+1)/2);
	for(int j=1;j<i;j++)
	    if(v[i]%v[j]==0) f[i]=(f[i]-f[j])%Mo;
	if(x&1) ans=(ans+1LL*x*f[i])%Mo;
	else ans=(ans+1LL*x*Pow(2,Mo-2)%Mo*f[i])%Mo;
    }
    cout<<(ans+Mo)%Mo;
    return 0;
}