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 mod=1e9+7;
int qpow(int x,int y){
	int res=1;
	for (;y;y>>=1,x=1LL*x*x%mod)
		if (y&1) res=1LL*res*x%mod;
	return res;
}
inline int upd(int x){return x+(x>>31&mod);}

int n,k;
int d[10000],dtot;
int f[10000];
int main()
{
	scanf("%d%d",&n,&k);
	for (int i=1;i*i<=n;i++)
		if (n%i==0){
			d[++dtot]=i;
			if (i*i!=n) d[++dtot]=n/i;
		}
	sort(d+1,d+dtot+1);
	int ans=0;
	for (int i=1;i<=dtot;i++){
		int x=d[i];
		f[i]=qpow(k,x+1>>1);
		for (int j=1;j<i;j++) if (d[i]%d[j]==0) f[i]=upd(f[i]-f[j]);
		if (x&1) ans=(ans+1LL*f[i]*x)%mod;
		else ans=(ans+1LL*(x/2)*f[i])%mod;
	}
	printf("%d\n",ans);
	return 0;
}