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<cstdio>
#include<algorithm>
using namespace std;
typedef long long ll;
const int N=100100,P=1000000007;
int i,j,k,n,m,nm,ans;
int a[N],f[N];
int ksm(int x,int y) {
	int z=1;
	for (;y;y>>=1,x=(ll) x*x%P) if (y&1) z=(ll) z*x%P;
	return z;
}
int main() {
	scanf("%d%d",&n,&m);
	for (i=1;i*i<=n;i++) if (n%i==0) {
		a[++nm]=i;
		if (i*i<n) a[++nm]=n/i;
	}
	sort(a+1,a+nm+1);
	for (i=1;i<=nm;i++) {
		f[i]=ksm(m,(a[i]+1)/2);
		for (j=1;j<i;j++) if (a[i]%a[j]==0) f[i]=(f[i]+P-f[j])%P;
	}
	for (i=1;i<=nm;i++) {
		if (a[i]&1) ans=((ll) f[i]*a[i]+ans)%P;
		else ans=((ll) f[i]*a[i]/2+ans)%P;
	}
	printf("%d\n",ans);
}