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 <iostream>
#include <vector>
#include <algorithm>

using namespace std;

const int MOD = 1000000007;

long long modPow(int a, int p){
	if(p == 0) return 1;
	long long res = modPow(a, p/2);
	res *= res;
	res %= MOD;
	if(p%2){
		res *= a;
		res %= MOD;
	}
	return res;
}

int main(){
	int N, K;
	while(cin >> N >> K){
		if(N == 1){
			cout << K << endl;
			continue;
		}
		vector<int> d;
		for(int i=1;i*i<=N;++i){
			if(N%i == 0){
			   d.push_back(i);
			   if(N/i != i) d.push_back(N/i);
			}
		}
		sort(d.begin(), d.end());
		vector<long long> num(d.size(), 0);
		long long res = 0;
		for(int i=0;i<d.size();i++){
			long long cycle = d[i];
			num[i] = modPow(K, (cycle+1)/2);
			for(int j=0;j<i;j++){
				if(cycle%d[j] == 0) num[i] = (num[i]+MOD-num[j])%MOD;
			}
			if(cycle%2 == 0) cycle /= 2;
			res += num[i] * cycle;
			res %= MOD;
		}
		cout << res << endl;
	}
}

