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 int long long
int a[2005], dp[2005];
int mod = 1e9 + 7;
int binpow(int a, int b){
	if (b == 0) return 1;
	int x = binpow(a, b / 2);
	x *= x; x %= mod;
	if (b % 2) return (x * a) % mod;
	else return x;
}
signed main(){
	int n, k; cin >> n >> k;
	int cur = 0;
	for (int i = 1; i <= sqrt(n); i++){
		if (n % i == 0){
			a[cur] = i; cur++;
			if (i * i != n){
				a[cur] = n / i; cur++;
			}
		}
	}
	sort(a, a + cur);
	for (int i = 0; i < cur; i++){
		dp[i] = binpow(k, (a[i] + 1) / 2);
		for (int j = 0; j < i; j++){
			if (a[i] % a[j] == 0){
				((dp[i] -= dp[j]) += mod) %= mod;
			}
		}
	}
	int ans = 0;
	for (int i = 0; i < cur; i++){
		if (a[i] % 2) (ans += (dp[i] * a[i])) %= mod;
		else (ans += (dp[i] * (a[i] / 2))) %= mod;
	}
	cout << ans;
}
