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;

const int MOD = 1000000007;

int pow_mod(int x, int k) {
	int ans = 1;
	while (k) {
		if (k&1) ans = 1LL * ans * x % MOD;
		x = 1LL * x * x % MOD;
		k >>= 1;
	}
	return ans;
}

int n, k;

int fac[222222], fn, dp[222222];

int cal() {
	fn = 0;
	for (int i = 1; i * i <= n; i++) {
		if (n % i == 0) {
			fac[++fn] = i;
			fac[++fn] = n / i;
		}
	}
	sort(fac + 1, fac + fn + 1);
	fn = unique(fac + 1, fac + 1 + fn) - fac - 1;
	for (int i = 1; i <= fn; i++) {
		if (n % 2 == 0 && n / 2 % fac[i] == 0) dp[i] = pow_mod(k, fac[i]);
		else dp[i] = pow_mod(k, (fac[i] + 1) / 2);
		for (int j = 1; j < i; j++) {
			if (fac[i] % fac[j] == 0) {
				dp[i] = (dp[i] - dp[j] + MOD) % MOD;
			}
		}
	}
	int ans = 0;
	for (int i = 1; i <= fn; i++) ans = (ans + 1LL * dp[i] * fac[i] % MOD) % MOD;
	return ans;
}

int main() {
	scanf("%d%d", &n, &k);
	printf("%d\n", cal());
	return 0;
}
