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<cstdio>
#include<algorithm>
#include<vector>
using namespace std;
long long Mod = 1000000007, n, K, C[101000];
vector<long long>V;
long long Pow(long long a, long long b) {
	long long r = 1;
	while (b) {
		if (b & 1)r = r*a%Mod;
		a = a*a%Mod; b >>= 1;
	}
	return r;
}
long long Get(long long a) {
	return Pow(K, (a + 1) / 2);
}
int main() {
	int i, j;
	scanf("%lld%lld", &n, &K);
	for (i = 1; i*i <= n; i++) {
		if (n%i == 0) {
			V.push_back(i);
			if (i*i != n)V.push_back(n / i);
		}
	}
	sort(V.begin(), V.end());
	int sz = V.size();
	long long res = 0;
	for (i = 0; i < sz; i++) {
		C[i] = Pow(K, (V[i] + 1) / 2);
		for (j = 0; j < i; j++) {
			if (V[i] % V[j] == 0)C[i] = (C[i]-C[j]+Mod)%Mod;
		}
		long long t = C[i] * V[i];
		if (V[i] % 2 == 0)t /= 2;
		res = (res + t) % Mod;
	}
	printf("%lld\n", res);
}