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 <vector>
#include <iostream>
#include <algorithm>
using namespace std;
const int mod = 1000000007;
int binpow(int a, int b) {
	int ret = 1;
	while (b) {
		if (b & 1) ret = 1LL * ret * a % mod;
		a = 1LL * a * a % mod;
		b >>= 1;
	}
	return ret;
}
int N, K;
int main() {
	cin >> N >> K;
	vector<int> d;
	for (int i = 1; i * i <= N; i++) {
		if (N % i == 0) {
			d.push_back(i);
			if (i * i != N) d.push_back(N / i);
		}
	}
	sort(d.begin(), d.end());
	vector<int> dp(d.size());
	int ret = 0;
	for (int i = 0; i < d.size(); i++) {
		dp[i] = binpow(K, (N % 2 == 0 && (N / 2) % d[i] == 0 ? d[i] : (d[i] + 1) / 2));
		for (int j = 0; j < i; j++) {
			if (d[i] % d[j] == 0) {
				dp[i] -= dp[j];
				if (dp[i] < 0) dp[i] += mod;
			}
		}
		ret = (ret + 1LL * dp[i] * d[i]) % mod;
	}
	cout << ret << endl;
	return 0;
}