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>
/*
Miku
*/
using namespace std;
typedef long long ll ;
const ll mk = 100005;
#define endl "\n"
const int mod = 1e9 + 7;
int n,k,a[2000],t,f[2000],i,j,l,ans;
inline int Mikuplaying(int x,int y){
    int ans=1;
	for(;y;y>>=1,x=1ll*x*x%mod) if(y&1)ans=1ll*ans*x%mod;return ans;
}
int main(){
	cin >> n >> k; 
	for(i=1;i*i<=n;++i)if(n%i==0){a[++t]=i;if(i*i !=n)a[++t]=n/i;}
	std::sort(a+1,a+t+1);
	for(j=1;j<=t; ans=(ans+1ll*f[j]*(a[j]&1?a[j]:a[j]/2))%mod,++j)
		for(f[j]=Mikuplaying(k,a[j]+1>>1),l=1;l<j;++l)if(a[j]%a[l]==0)f[j]=(f[j]+mod-f[l])%mod;
	cout << ans;
	return 0;
}