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;
using lint = long long int;
lint MOD = 1000000007;

template <typename T>
T power(T x, T n, T mod) {
    T ans = 1;
    while (n>0)
    {
        if (n & 1) ans = ans * x % mod;
        x = x * x % mod;
        n >>= 1;
    }
    return ans;
}

int N;
lint K;

int main()
{
    cin >> N >> K;

    vector<lint> divs;
    for (int d=1; d*d<=N; d++)
    {
        if (N % d == 0) divs.push_back(d);
    }
    for (int i = divs.size()-1; i>=0; i--)
    {
        if (divs.back() != N / divs[i]) divs.push_back(N / divs[i]);
    }

    vector<lint> w(divs.size());

    lint ans = 0;
    for (int i=0; i<divs.size(); i++)
    {
        lint d = divs[i];
        lint tmp = power(K, (d + 1)/2, MOD);
        for (int j=0; j<i; j++)
        {
            if (divs[i] % divs[j]) continue;
            tmp = (tmp - w[j] + MOD) % MOD;
        }
        w[i] = tmp;
        ans = (ans + tmp * ((d&1) ? d : d/2 )) % MOD; 
    }
    cout << ans << endl;
}
