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<cstring>
#include<algorithm>
#include<cmath>
#define mod 1000000007
using namespace std;
int n,K;
int fac[100010],cnt;
int f[100010];
int quick_pow(int x,int p)
{
    int an=1,po=x;
    while(p)
    {
        if(p&1)  an=1ll*an*po%mod;
        po=1ll*po*po%mod;
        p>>=1;
    }
    return an;
}
int ans;
int main()
{
    cin>>n>>K;
    for(int i=1;i<=sqrt(n);i++)
    {
        if(n%i==0)
        {
            fac[++cnt]=i;
            if(n/i!=i)  fac[++cnt]=n/i;
        }
    }
    sort(fac+1,fac+cnt+1);
    for(int i=1;i<=cnt;i++)
    {
        f[i]=quick_pow(K,(fac[i]+1)/2);
        for(int j=1;j<i;j++)
        {
            if(fac[i]%fac[j]==0)  f[i]=(f[i]-f[j]+mod)%mod;
        }
        if(fac[i]&1)  ans=(ans+1ll*fac[i]*f[i]%mod)%mod;
        else          ans=(ans+1ll*(fac[i]>>1)*f[i]%mod)%mod;
    }
    cout<<ans<<endl;
    return 0;
}