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
const int mod=1e9+7,N=2e5+20;
ll n,k,dp[2500];
int qpow(ll x,int k){
	ll ans=1;
	while(k){
		if(k&1) ans*=x;
		k>>=1,x*=x;
		ans%=mod,x%=mod;
	}
	return ans;
}
int v[3000],cnt;
void init(){
	for(ll i=1;i*i<=n;i++)if(n%i==0){
		v[++cnt]=i;
		if(i*i!=n) v[++cnt]=n/i;
	}
	sort(v+1,v+cnt+1);
}
int main()
{
	cin>>n>>k;
	init();
	ll ans=0;
	for(int x=1;x<=cnt;x++){
		dp[x]=qpow(k,(v[x]+1)/2);
		for(int y=1;y<x;y++){
			if(v[x]%v[y]==0)
				dp[x]=(dp[x]-dp[y]+mod)%mod;	
		}	
		if(v[x]%2)
			ans=(ans+(dp[x]*v[x])%mod)%mod;
		else
			ans=(ans+(dp[x]*v[x]/2)%mod)%mod;
	}
	cout<<ans<<endl;
	return 0;
}