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> d, f;
int n, k;

int qpow(int a,int exp) {
	int ans = 1;
	while(exp)  {
		if(exp & 1) ans = ans * a % mod;
		a = a * a % mod;  exp >>= 1;
	}
	return ans;
}
 
signed main()   {
	ios_base::sync_with_stdio(false);
	cin.tie(0); cout.tie(0);
	
	cin >> n >> k;
	
	for(int i = 1 ; i * i <= n ; ++i) 
		if (n % i == 0) {
			d.push_back(i);
			if (i < (n / i)) 
				d.push_back(n / i);	
		}
	sort(d.begin(),d.end());
	
	f.resize(d.size());
	
	int ans = 0;
	
	for(int i = 0 ; i < d.size() ; ++i) {
		f[i] = qpow(k,(d[i] + 1) / 2);
		for(int j = 0 ; j < i ; ++j)
			if(d[i] % d[j] == 0)
				f[i] = (f[i] - f[j] + mod) % mod;
		ans = (ans + f[i] * (d[i] & 1 ? d[i] : d[i] / 2)) % mod;
	}
	
	cout << ans << endl;
}