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 int long long
const int mod=1e9+7;
vector<int> divi;
int dp[2005];
int pow(int a,int b,int mod){
	if(b==1){
		return a;
	}
	int k=pow(a,b/2,mod)%mod;
	if(b%2==0){
		return (k*k)%mod;
	}
	return ((k*k)%mod*a)%mod;
}
signed main(){
	int n,k,ans=0;
	cin>>n>>k;
	for(int i=1;i<=sqrt(n);i++){
		if(n%i==0){
			divi.push_back(i);
			divi.push_back(n/i);
			if(i*i==n){
				divi.pop_back();
			}
		}
	}
	sort(divi.begin(),divi.end());
	for(int i=0;i<divi.size();i++){
		dp[i]=pow(k,(divi[i]+1)/2,mod);
		for(int j=0;j<i;j++){
			if(divi[i]%divi[j]==0){
				dp[i]=(dp[i]-dp[j]+mod)%mod;
			}
		}
		if(divi[i]%2==0){
			ans+=1LL*dp[i]*divi[i]/2;
			ans%=mod;
		}
		else{
			ans+=1LL*dp[i]*divi[i];
			ans%=mod;
		}
	}
	cout<<ans;
}