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 MOD (1000000007)
#define LL long long
using namespace std;

LL n,k,ans;
vector<LL>v,f;

LL Qpow(LL a,LL b)
{
	LL ans=1;
	while (b)
	{
		if (b&1) ans=ans*a%MOD;
		a=a*a%MOD; b>>=1;
	}
	return ans;
}

int main()
{
	cin>>n>>k;
	for (int i=1; i<=sqrt(n); ++i)
		if (n%i==0)
		{
			v.push_back(i);
			if (n/i!=i) v.push_back(n/i);
		}
	sort(v.begin(),v.end());
	f.resize(v.size());
	for (int i=0,sz=v.size(); i<sz; ++i)
	{
		f[i]=Qpow(k,(v[i]+1)/2);
		for (int j=0; j<i; ++j)
			if (v[i]%v[j]==0) (f[i]-=f[j])%=MOD;
		if (v[i]%2) (ans+=f[i]*v[i]%MOD)%=MOD;
		else (ans+=f[i]*v[i]/2%MOD)%=MOD;
	}
	cout<<(ans+MOD)%MOD<<endl;
}