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;
int n, k;
const int MOD = 1e9 + 7;
const int N = 1000000;
int ans[N], finans;
vector <int> V;
int powi(int a, int b)
{
    int c = 1;
    for (; b; b >>= 1, a = 1ll * a * a % MOD)
        if (b & 1) c = 1ll * c * a % MOD;
    return c;
}
int main()
{
    cin >> n >> k;
    for (int 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());
    for (int i = 0; i < V.size(); ++ i)
    {
        ans[i] = powi(k, (V[i] + 1) / 2);
        for (int j = 0; j < i; ++ j) if (V[i] % V[j] == 0)
            ans[i] = (ans[i] - ans[j] + MOD) % MOD;
        finans = (finans + 1ll * ans[i] * (V[i] & 1? V[i]: V[i] / 2)) % MOD;
    }
    cout << finans << endl;
}