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 int long long
const int M=1e9+7;
int n,k,a[100005],ans;
vector<int> v;
int ksm(int x,int y){
	int ans=1;
	for (;y;y>>=1,x=x*x%M)
		if (y&1)(ans*=x)%=M;
	return ans;
}
signed main(){
	scanf("%lld%lld",&n,&k);
	for (int i=1;i*i<=n;i++)
		if (n%i==0){
			v.push_back(i);
			if (i*i!=n)v.push_back(n/i);
		}
	sort(v.begin(),v.end());
	for (int i=0;i<(int)v.size();i++){
		a[i]=ksm(k,(v[i]+1)/2);
		for (int j=0;j<i;j++)
			if (v[i]%v[j]==0)(a[i]+=M-a[j])%=M;
		if (v[i]&1)(ans+=v[i]*a[i])%=M;
		else (ans+=v[i]/2*a[i])%=M;
	}
	printf("%lld\n",ans);
}
