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;

#define pb push_back
typedef vector<int> vi;

const int mod = 1e9 + 7;
int n, K, ans;
vi prime, dp;

int fpow(int a, int m) {
    int res = 1;
    for(; m; m >>= 1, a = (1LL * a * a) % mod) if(m & 1) res = (1LL * res * a) % mod;
    return res;
}

int main () {
    ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
    cin >> n >> K;
    for (int i = 1; i * i <= n; ++i) {
        if(n % i == 0) {
            prime.pb(i);
            if(i < n / i) prime.pb(n / i);
        }
    }
    sort(prime.begin(), prime.end() );
    dp.resize(prime.size() );

    for(int i = 0; i < prime.size(); ++i) {
        dp[i] = fpow(K, (prime[i] + 1) >> 1);
        for(int j = 0; j < i; ++j) {
            if( (prime[i] % prime[j]) == 0) dp[i] -= dp[j], dp[i] %= mod;
        }
        ans += (1LL * (prime[i] & 1 ? prime[i] : prime[i] >> 1) * dp[i]) % mod;
        ans %= mod;
    }

    cout << (ans + mod) % mod;

    return 0;
}
