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 int

const int mod=1e9+7;

ll p(ll a,ll b){
	a%=mod;
	ll res=1;
	while(b){
		if(b&1)	res=res*a%mod;
		a=a*a%mod;
		b>>=1;
	}
	return res;
}

vector<ll> d,f;
int main(){
	ios_base::sync_with_stdio(0);
	cin.tie(0);
	int n,k;
	cin>>n>>k;
	for(int i=1;i*i<=n;i++){
		if(n%i==0){
			d.emplace_back(i);
			if(i*i!=n)
				d.emplace_back(n/i);
		}
	}
	sort(d.begin(),d.end());
	ll ans=0;
	for(int i=0;i<d.size();i++){
		f.emplace_back(p(k,(d[i]+1)/2));
		for(int j=0;j<i;j++)
			if(d[i]%d[j]==0)
				f[i]=f[i]-f[j]+mod;
		f[i]%=mod;
		if(d[i]%2==0)
			ans=(ans+d[i]*f[i]%mod*p(2,mod-2))%mod;
		else
			ans=(ans+d[i]*f[i])%mod;
	}
	cout<<ans<<endl;

}
