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<iostream>
#include<set>
#include<unordered_map>
using namespace std;

#define mod 1000000007

int n, k, ans;

int qpow(int a, int b)
{
	int res = 1;
	while (b)
	{
		if (b & 1)res = (long long)res * a % mod;
		a = (long long)a * a % mod;
		b >>= 1;
	}
	return res;
}

int main()
{
	scanf("%d%d", &n, &k);
	set<int> v;
	unordered_map<int, int> s;
	for (int i = 1; i * i <= n; ++i)
		if (n % i == 0)
		{
			v.insert(i);
			if (i * i != n)v.insert(n / i);
		}
	for (auto x : v)
	{
		int res = qpow(k, (x + 1) / 2);
		for (int i = 1; i * i <= x; ++i)
			if (x % i == 0)
			{
				res -= s[i];
				if (res < 0)res += mod;
				if (i * i != x)
				{
					res -= s[x / i];
					if (res < 0)res += mod;
				}
			}
		s[x] = res;
		ans += (long long)res * (x % 2 ? x : x / 2) % mod;
		if (ans >= mod)ans -= mod;
	}
	printf("%d\n", ans);
}