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;

#define mod 1000000007

int n,k,ans;

int qpow(int a,int b)
{
	int res=1;
	while(b)
	{
		if(b&1)res=(long long)res*a%mod;
		a=(long long)a*a%mod;
		b>>=1;
	}
	return res;
}

int main()
{
	scanf("%d%d",&n,&k);
	set<int> v;
	unordered_map<int,int> s;
	for(int i=1;i*i<=n;++i)
		if(n%i==0)
		{
			v.insert(i);
			if(i*i!=n)v.insert(n/i);
		}
	for(auto x : v)
	{
		int res=qpow(k,(x+1)/2);
		for(int i=1;i*i<=x;++i)
			if(x%i==0)
			{
				res-=s[i];
				if(res<0)res+=mod;
				if(i*i!=x)
				{
					res-=s[x/i];
					if(res<0)res+=mod;
				}
			}
		s[x]=res;
		ans+=(long long)res*(x%2?x:x/2)%mod;
		if(ans>=mod)ans-=mod;
	}
	printf("%d\n",ans);
}