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;

#define ll long long
#define P 1000000007 

ll n,k,dp[33335];

vector<ll> fac;

ll fpow(ll a,ll b){
	ll c=1;
	for(;b;b>>=1,a=a*a%P)
		if(b&1) c=c*a%P;
	return c;
}

void work()
{
	ll ans=0;
	for(int x=0;x<fac.size();x++){
		dp[x]=fpow(k,(fac[x]+1)/2);
		for(int y=0;y<x;y++){
			if(fac[x]%fac[y]==0)
				dp[x]=(dp[x]-dp[y]+P)%P;
		}
		if(fac[x]%2) ans=(ans+dp[x]*fac[x]%P)%P; 
        else ans=(ans+dp[x]*fac[x]/2%P)%P;
	}
    cout<<ans<<endl;  
}

void init()
{
	fac.clear();
	for(ll i=1;i*i<=n;i++){
        if(n%i==0){
            fac.push_back(i);
            if(i*i!=n) fac.push_back(n/i);
        }
    }
    sort(fac.begin(),fac.end());
}

int main()
{
	while(cin>>n>>k) init(),work();
    return 0;
}