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>
#include <map>
using namespace std;
typedef long long ll;
constexpr ll mod = 1000000007;
vector<ll> v;
ll cnt[2010] = {};
ll pw(ll a,ll x){
    ll ret = 1;
    while(x){
        if(x&1) (ret *= a) %= mod;
        (a *= a) %= mod; x /= 2;
    }
    return ret;
}

int main(){
    ll i,j,n,k; cin >> n >> k;
    for(i=1;i*i<=n;i++){
        if(n%i==0){
            v.push_back(i);
            if(i*i!=n) v.push_back(n/i);
        }
    }
    sort(v.begin(),v.end());
    for(i=0;i<v.size();i++){
        ll num = pw(k,(v[i] + 1)/2);
        for(j=0;j<i;j++){
            if(v[i]%v[j]==0){
                num -= cnt[j];
                if(num<0) num += mod;
            }
        }
        cnt[i] = num;
    }
    ll ans = 0;
    for(i=0;i<v.size();i++){
        if(v[i]&1) (ans += v[i]*cnt[i]%mod) %= mod;
        else (ans += v[i]/2*cnt[i]%mod) %= mod;
    }
    cout << ans << endl;
}