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 ll = long long;

const ll MOD = ll(1e9 + 7);
const int K = 2333;

int n, k;
ll f[K];

ll pw(ll a, ll b) {
    ll r = 1;
    for (; b > 0; b >>= 1) {
        if (b & 1) {
            r = r * a % MOD;
        }
        a = a * a % MOD;
    }
    return r;
}

int main() {
    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());
    assert(int(divs.size()) < K);

    ll ans = 0;
    for (int i = 0; i < int(divs.size()); i++) {
        int d = divs[i];
        f[i] = pw(k, (d + 1) / 2);
        for (int j = 0; j < i; j++) {
            if (d % divs[j] == 0) {
                f[i] = (f[i] - f[j] + MOD) % MOD;
            }
        }

        ll coef = (d % 2 == 0 ? d / 2 : d);
        ans = (ans + coef * f[i]) % MOD;
    }

    cout << ans << endl;
}