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>
#define be(v) (v).begin(),(v).end()
#define pb(q) push_back(q)
typedef long long ll;
using namespace std;
const ll mod=1000000007, INF=mod*mod*3LL;
#define doublecout(a) cout<<fixed<<setprecision(10)<<a<<endl;

long long modpow(long long a, long long n) {
    long long res = 1;
    while (n > 0) {
        if (n & 1) res = res * a % mod;
        a = a * a % mod;
        n >>= 1;
    }
    return res;
}

int main() {
    cin.tie(0);
    cout.tie(0);
    ios::sync_with_stdio(false);
    ll n, k, ans = 0;
    cin >> n >> k;
    set<ll> s;
    map<ll,ll> mp;
    for(int i=1;i*i<=n;i++)if(n%i==0)s.insert(i),s.insert(n/i);
    for(auto& i:s){
    	mp[i] = modpow(k,(i+1)/2);
    	for(auto& j:s){
    		if(i<=j) continue;
    		if(i % j == 0) (mp[i] -= mp[j]) %= mod;
    	}
    	ans += mp[i]*(i&1?i:i/2)%mod;
    	ans %= mod;
    }
    ans += mod;
    cout << ans%mod << endl;
    return 0;
}
