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 maxn 50009
using namespace std;
const int MOD=1e9+7;
int n,m;
vector<int>G;
long long f[maxn],g[maxn];
void div(int n){
	for(int i=1;i*i<=n;i++){
		if(n%i)
			continue;
		G.push_back(i);
		if(i*i!=n)
			G.push_back(n/i);
	}
	sort(G.begin(),G.end());
}
long long mgml(long long a,int b){
	long long res=1;
	while(b){
		if(b&1)
			res=res*a%MOD;
		a=a*a%MOD;
		b>>=1;
	}
	return res;
}
int main(){
	cin>>n>>m;
	div(n);
	int sz=G.size();
	for(int i=0;i<sz;i++){
		f[i]=mgml(m,(G[i]+1)/2);
	}
	for(int i=0;i<sz;i++){
		g[i]=f[i];
		for(int j=0;j<i;j++){
			if(G[i]%G[j]==0){
				g[i]-=g[j];
				g[i]%=MOD;
				g[i]+=MOD;
				g[i]%=MOD;
			}
		}
	}
	long long ans=0;

		for(int i=0;i<sz;i++){
			if(G[i]%2==0){
				g[i]=g[i]*mgml(2,MOD-2)%MOD;
			}
			ans=(ans+g[i]*G[i])%MOD;
		}
	
	cout<<ans<<endl;
	//system("pause");
	return 0;
}