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 <iostream>
#include <vector>
#include <algorithm>
using namespace std;
using ll = long long int;

const ll MOD = 1000000007;
ll mod_pow(ll N, ll K) {
    ll ret = 1;
    for(; K>0; K>>=1) {
        if(K & 1) (ret *= N) %= MOD;
        (N *= N) %= MOD;
    }
    return ret;
}

using ll = long long int;
int main() {
    ll N, K, ans = 0, inv2 = mod_pow(2, MOD-2); cin >> N >> K;
    vector<ll> div, num;
    for(int k=1; k*k<=N; k++) {
        if(N % k == 0) {
            div.push_back(k);
            if(N / k != k) div.push_back(N / k);
        }
    }
    sort(div.begin(), div.end());
    int M = div.size(); num.resize(M);
    for(int i=0; i<M; i++) {
        num[i] = mod_pow(K, (div[i] + 1) / 2);
        for(int j=0; j<i; j++) if(div[i] % div[j] == 0) {
            num[i] = (num[i] - num[j] + MOD) % MOD;
        }
        if(div[i] % 2 == 1) (ans += div[i] * num[i]) %= MOD;
        else (ans += div[i] * num[i] % MOD * inv2) %= MOD;
    }
    cout << ans << endl;
    return 0;
}