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 fo(i,j,l) for(int i=j;i<=l;++i)
#define fd(i,j,l) for(int i=j;i>=l;--i)

using namespace std;
typedef long long ll;
const ll N=2e5,mo=1e9+7;

int n,o,p;
ll f[N],a[N],k;

ll ksm(ll o,ll t)
{
	ll y=1;
	for(;t;t>>=1,o=o*o%mo)
	if(t&1)y=y*o%mo;
	return y;
}

int main()
{
	cin>>n>>k;
	for(int i=1;i*i<=n;++i)
	if(n%i==0){
		a[++o]=i;
		if(i*i%n)a[++o]=n/i;
	}
	sort(a+1,a+o+1); 
	ll ans=0;
	fo(i,1,o){
		f[i]=ksm(k,(a[i]+1)>>1);
		fo(l,1,i-1)if(a[i]%a[l]==0)f[i]=(f[i]-f[l]+mo)%mo;
		(a[i]&1)?ans=(ans+f[i]*a[i])%mo:ans=(ans+(f[i]*a[i]>>1))%mo;
	}
	cout<<ans;
}