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>
#define pb push_back

using namespace std;
typedef long long ll;

const int P=1e9+7,N=2333;
int fpow(int a,int t){static int r;for(r=1;t;t>>=1,a=(ll)a*a%P)if(t&1)r=(ll)r*a%P;return r;}

int n,k,m,ve[N],f[N],ans;

int main(){
	scanf("%d%d",&n,&k);
	for(int i=1;i*i<=n;i++)if(n%i==0){ve[++m]=i;if(i*i<n)ve[++m]=n/i;}
	sort(ve+1,ve+m+1);
	for(int i=1;i<=m;i++){
		f[i]=fpow(k,(ve[i]+1)/2);
		for(int j=1;j<i;j++)if(ve[i]%ve[j]==0)f[i]=(f[i]-f[j]+P)%P;
		if(ve[i]&1)ans=(ans+(ll)ve[i]*f[i])%P;
		else ans=(ans+(ll)(ve[i]>>1)*f[i])%P;
	}
	printf("%d\n",ans);
	return 0;
}