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>
const long long MOD = 1000000007;
int N, K, d[10000], w[10000], L;
long long O;
long long POWER(long long a, long long b)
{
	long long r = 1;
	for (; b; b >>= 1)
	{
		if (b & 1)
			r = r * a % MOD;
		a = a * a % MOD;
	}
	return r;
}
int main()
{
	scanf("%d%d", &N, &K);
	for (int i = 1; i * i <= N; i++)
		if (N % i == 0)
		{
			d[L++] = i;
			if (i * i < N)
				d[L++] = N / i;
		}
	std::sort(d, d + L);
	for (int i = 0; i < L; i++)
		w[i] = d[i];
	for (int i = L - 1; i >= 0; i--)
		for (int j = i + 1; j < L; j++)
			if (d[j] % d[i] == 0)
				w[i] -= w[j];
	for (int i = 0; i < L; i++)
		O = (O + (w[i] + MOD) * POWER(K, N / d[i] & 1 ? d[i] + 1 >> 1 : d[i])) % MOD;
	printf("%lld\n", O);
	return 0;
}
