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 ll = long long;

const int MAXD = 2333;
const int MOD = 1e9 + 7;
int N, K;
int dp[MAXD];

int powmod(int a, int b) {
	int r = 1;
	while (b) {
		if (b & 1) {
			r = ll(r) * a % MOD;
		}
		a = ll(a) * a % MOD;
		b /= 2;
	}
	return r;
}

int main() {
	cin >> N >> K;

	vector<int> factors;
	for (int i = 1; i*i <= N; i++) {
		if (N % i == 0) {
			factors.push_back(i);
			if (i*i != N) {
				factors.push_back(N / i);
			}
		}
	}
	sort(factors.begin(), factors.end());

	for (size_t i = 0; i < factors.size(); i++) {
		dp[i] = powmod(K, (factors[i]+1)/2);
		for (size_t j = 0; j < i; j++) {
			if (factors[i] % factors[j]) continue;
			dp[i] -= dp[j];
			if (dp[i] < 0) dp[i] += MOD;
		}
	}

	int ans = 0;
	for (size_t i = 0; i < factors.size(); i++) {
		if (factors[i] % 2 == 0) {
			ans = (ans + ll(dp[i]) * factors[i] / 2) % MOD;
		} else {
			ans = (ans + ll(dp[i]) * factors[i]) % MOD;
		}
	}
	cout << ans << endl;

	return 0;
}