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;
const int mod=1e9+7;
int ans;
int fastpow(int x,int a){
	int ret=1;
	while(a){
		if(a&1) ret=ret*1LL*x%mod;
		x=x*1LL*x%mod;a>>=1;
	}
	return ret;
}

int ys[50005],yscnt;
int num[50005];
int main(){
	int n,k;
	cin>>n>>k;
	for(int i=1;i*i<=n;i++){
		if(n%i==0){
			ys[++yscnt]=i;
			if(i*i!=n) ys[++yscnt]=n/i;
		}
	}
	sort(ys+1,ys+yscnt+1);
	for(int i=1;i<=yscnt;i++){
		num[i]=(num[i]+fastpow(k,(ys[i]+1)/2) )%mod;
		for(int j=i+1;j<=yscnt;j++) if(ys[j]%ys[i]==0) num[j]=(num[j]-num[i])%mod;
	}
	for(int i=1;i<=yscnt;i++){
		//if(n%2==0&&ys[i]%2!=0) continue;
		ans=(ans+num[i]*1LL*(ys[i]%2==0? ys[i]/2:ys[i]))%mod;
	}
	cout<<(ans+mod)%mod<<endl;
	return 0;
}