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<cmath>
#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
using namespace std;
const int MOD = 1000000007;
int n, k, len, i, j, a[50005], f[50005], ans;
inline int ksm(int x, int y, int z)
{
	int b = 1;
	while (y)
	{
		if (y & 1) b = 1ll * b * x % z;
		x = 1ll * x * x % z;
		y >>= 1;
	}
	return b;
}
int main()
{
	cin >> n >> k;
	for(i = 1; i * i <= n; i ++)
		if (n % i == 0)
		{
			a[++len] = i;
			if (n / i != i) a[++len] = n / i;
		}
	sort(a + 1, a + 1 + len);
	int inv2 = (MOD + 1) >> 1;
	for(i = 1; i <= len; i ++)
	{
		f[i] = ksm(k, (a[i] + 1) >> 1, MOD);
		for(j = 1; j < i; j ++)
			if (a[i] % a[j] == 0) f[i] = (f[i] + MOD - f[j]) % MOD;
		if (a[i] & 1) ans = (ans + 1ll * f[i] * a[i]) % MOD;
		else ans = (ans + 1ll * f[i] * a[i] % MOD * inv2) % MOD;
	}
	cout << ans << endl;
}