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;

const int64_t MOD = 1e9+7;
void add(int64_t& a, int64_t b){
    a = (a+b) % MOD;
}
void mul(int64_t& a, int64_t b){
    a = a*b % MOD;
}

int64_t power_mod(int64_t num, int64_t power){
    int64_t prod = 1;
    num %= MOD;
    while(power > 0){
        if(power&1) prod = prod * num % MOD;
        num = num * num % MOD;
        power >>= 1;
    }
    return prod;
}

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 < N/i) divs.push_back(N/i);
    }
    sort(divs.begin(), divs.end());
    int sz = divs.size();

    vector<int64_t> num(sz);
    int64_t ans = 0;
    for(int i=0; i<sz; i++){
        int d = divs[i];
        int64_t res = power_mod(K, (d+1)/2);
        add(num[i], res);
        add(ans, num[i] * (d%2 ? d : d/2));
        for(int j=i+1; j<sz; j++) if(divs[j] % divs[i] == 0) add(num[j], MOD - num[i]);
    }
    cout << ans << endl;
    return 0;
}
