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 <cstring>
#include <algorithm>
using namespace std;
const int mod=1000000007;
int num[2000],fac[2000],cnt;

int add(int x,int y)
{return (x+y)%mod;}
int sub(int x,int y)
{return (x-y+mod)%mod;}
int mul(int x,int y)
{return 1LL*x*y%mod;}
int fpow(int x,int y)
{
	int ans=1;
	while(y)
	{
		if(y&1)ans=mul(x,ans);
		y>>=1,x=mul(x,x);
	}
	return ans;
}

int main()
{
	int n,k;
	scanf("%d%d",&n,&k);
	for(int i=1;i*i<=n;++i)
	  if(n%i==0)
	    {
	    	fac[++cnt]=i;
	    	if(i*i<n)
	    	  fac[++cnt]=n/i;
	    }
	sort(fac+1,fac+1+cnt);
	int ans=0;
	for(int i=1;i<=cnt;++i)
	{
		num[i]=fpow(k,(fac[i]+1)>>1);
		for(int j=1;j<i;++j)
		  if(fac[i]%fac[j]==0)
		    num[i]=sub(num[i],num[j]);
		if(fac[i]%2==0)ans=add(ans,mul(num[i],fac[i]>>1));
		else ans=add(ans,mul(num[i],fac[i]));
	}
	printf("%d\n",ans);
	return 0;
}