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;
int n,k;
map<int,int>mp;
const int p = 1000000007;
int pw(int x,int y)
{
    int lst=1;
    while(y)
    {
        if(y&1)lst=1LL*lst*x%p;
        y>>=1;
        x=1LL*x*x%p;
    }
    return lst;
}
int yin[100005],cnt;
int main()
{
    scanf("%d%d",&n,&k);
    for(int i=1;i*i<=n;i++)
    {
        if(n%i==0)
        {
            yin[++cnt]=i;
            if(i*i!=n)yin[++cnt]=n/i;
        }
    }
    int ans=0;
    sort(yin+1,yin+cnt+1);
    for(int i=1;i<=cnt;i++)
    {
        int tmp=pw(k,(yin[i]-1)/2+1);
        if(i!=1)
        for(int j=1;j*j<=yin[i];j++)
        {
            if(yin[i]%j==0)
            {
                tmp-=mp[j];
                if(j*j!=yin[i]&&j!=1)tmp-=mp[yin[i]/j];
                tmp=(tmp%p+p)%p;
            }
        }
        mp[yin[i]]=tmp;
        if(yin[i]%2==1)ans+=1LL*tmp*yin[i]%p;
        else ans+=1LL*tmp*yin[i]%p*500000004%p;
        ans%=p;
    }
    cout<<ans<<endl;
    return 0;
}
