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 <algorithm>
#include <iostream>
#include <unordered_map>
#include <vector>

using namespace std;

constexpr static int MOD = 1e9 + 7;

int64_t mpow(int64_t a, int64_t e) {
    int64_t r = 1, p = a;
    while (e) {
        if (e & 1)
            r = (r * p) % MOD;
        p = (p * p) % MOD;
        e >>= 1;
    }
    return r;
}

int64_t cnt[1 << 16];

int main() {
    int n, k;
    cin >> n >> k;

    vector <int> divs;
    for (int i = 1; i * i <= n; i++)
        if (n % i == 0) {
            divs.push_back(i);
            if (i * i != n)
                divs.push_back(n / i);
        }
    sort(divs.begin(), divs.end());

    int64_t total = 0;
    for (int i = 0; i < divs.size(); i++) {
        cnt[i] = mpow(k, (divs[i] + 1) / 2);
        for (int j = 0; j < i; j++)
            if (divs[i] % divs[j] == 0)
                cnt[i] = (cnt[i] - cnt[j] + MOD) % MOD;
        if (divs[i] % 2)
            total += cnt[i] * divs[i];
        else
            total += cnt[i] * (divs[i] / 2);
        total %= MOD;
    }
    cout << total << endl;
}
