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;
typedef long long ll;
const ll mod = 1e9 + 7;
const int maxn = 1e5 + 10;
ll n, k, ans;
vector<ll> d;
ll f[maxn];
ll powMod(ll a, ll k)
{
	ll ret = 1;
	while(k)
	{
		if(k & 1) ret = ret * a % mod;
		a = a * a % mod; k >>= 1;
	}
	return ret;
}
ll inv(ll a) { return powMod(a, mod - 2);}
int main()
{
	cin >> n >> k;
	for(ll i = 1; i * i <= n; ++i)
		if(n % i == 0)
		{
			d.push_back(i);
			if(i * i != n)
				d.push_back(n / i);
		}
	sort(d.begin(), d.end());
	for(int i = 0; i < d.size(); ++i)
	{
		int len = d[i];
		f[i] = powMod(k, (len + 1) / 2);
		for(int j = 0; j < i; ++j)
			if(d[i] % d[j] == 0)
				f[i] = (f[i] + mod - f[j]) % mod;
		ll tmp = f[i] * len % mod;
		if(len % 2 == 0) tmp = tmp * inv(2) % mod;
		ans = (ans + tmp) % mod;
	}
	cout << ans << endl;
	return 0;
}