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 P = 1e9 + 7;

int n, k, ans;
unordered_map<int, int>f;

int qp (int a, int b) { int c = 1; for (; b; b >>= 1, a = 1ll * a * a % P) if (b & 1) c = 1ll * c * a % P; return c; }

int d (int n) {
	if (f.count(n)) return f[n];
	int ret = qp(k, (n + 1) >> 1);
	for (int i = 1; i * i <= n; ++i) if (n % i == 0) {
		ret = (ret + P - d(i)) % P;
		if (i > 1 && i * i != n) ret = (ret + P - d(n / i)) % P;
	}
	return f[n] = ret;
}

void calc (int x) {
	int ret = d(x);
	if (!(x & 1)) x >>= 1;
	ans = (1ll * ret * x + ans) % P;
}

int main () {
	scanf("%d%d", &n, &k); f[1] = k;
	for (int i = 1; i * i <= n; ++i) if (n % i == 0) {
		calc(i);
		if (i * i != n) calc(n / i);
	}
	printf("%d\n", ans);
	return 0;
}