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;
using pi = pair<int, int>;
using lint = long long;
const int mod = 1e9 + 7;
const int MAXN = 100005;

int n, k;

lint ipow(int x, int p){
	lint ret = 1, piv = x;
	while(p){
		if(p & 1) ret = ret * piv % mod;
		piv = piv * piv % mod;
		p >>= 1;
	}
	return ret;
}

int main(){
	vector<int> yaksu;
	cin >> n >> k;
	for(int i=1; i*i<=n; i++){
		if(n % i == 0){
			yaksu.push_back(i);
			if(i * i != n) yaksu.push_back(n / i);
		}
	}
	sort(yaksu.begin(), yaksu.end());
	vector<lint> dp(yaksu.size());
	lint ret = 0;
	for(int i=0; i<dp.size(); i++){
		// dp[i] = (palindrome with exactly yaksu[i] period)
		dp[i] = ipow(k, (yaksu[i] + 1) / 2);
		for(int j=0; j<i; j++){
			if(yaksu[i] % yaksu[j] == 0){
				dp[i] += mod - dp[j];
			}
		}
		dp[i] %= mod;
		ret += dp[i] * (yaksu[i] % 2 ? yaksu[i] : (yaksu[i] / 2));
		ret %= mod;
	}
	cout << ret << endl;
}
