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
/**
6 3 -> 75
ababab
*/
#include <bits/stdc++.h>
using namespace std;

const int mod = 1e9 + 7;

int n, k;
vector<int> d, f;

void add(int &x,int y) {
	x += y;
	if (x >= mod) x -= mod;
}

int pw(int x,int y) {
	int ret = 1;
	while (y) {
		if (y & 1) ret = 1ll * ret * x % mod;
		x = 1ll * x * x % mod;
		y >>= 1;
	}
	return ret;
}

int main() {
	ios_base::sync_with_stdio(false);
	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] = pw(k, (d[i] + 1) >> 1);
		for (int j = 0; j < i; ++j) if (d[i] % d[j] == 0) {
			add(f[i], mod - f[j]);
		} 
		add(ans, 1ll * f[i] * (d[i] & 1 ? d[i] : d[i] >> 1) % mod);
	}
	cout << ans << '\n';
}