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=2010,MD=1e9+7;
int v[N],f[N];
int Pow(int x,int y)
{
    int ans=1;
    for(;y;x=x*1LL*x%MD,y>>=1)if(y&1)ans=1LL*ans*x%MD;
    return ans;
}
int main()
{
    int n,k,tot=0,ans=0,i;
    cin>>n>>k;
    for(i=1; i*i<n; i++)
        if(n%i==0)v[tot++]=i,v[tot++]=n/i;
    if(i*i==n)v[tot++]=i;
    sort(v,v+tot);
    for(int i=0; i<tot; i++)
    {
        f[i]=Pow(k,(v[i]+1)/2);
        for(int j=0; j<i; j++)if(v[i]%v[j]==0) f[i]=(f[i]-f[j])%MD;
        if(v[i]&1) ans=(ans+1LL*v[i]*f[i])%MD;
        else ans=(ans+v[i]*1LL*Pow(2,MD-2)%MD*f[i])%MD;
    }
    cout<<(ans+MD)%MD;
}
