Problem:
Score : 1000 points

Problem Statement

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.

Sample Input 1

4 2

Sample Output 1

6

The following six sequences can be obtained:

(1, 1, 1, 1)

(1, 1, 2, 2)

(1, 2, 2, 1)

(2, 2, 1, 1)

(2, 1, 1, 2)

(2, 2, 2, 2)

Sample Input 2

1 10

Sample Output 2

10

Sample Input 3

6 3

Sample Output 3

75

Sample Input 4

1000000000 1000000000

Sample Output 4

875699961

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
#define REP(i, n, s) for (LL i = (s); i < (n); i++)
#define MOD 1000000007
using namespace std;
typedef long long int LL;
typedef long double LD;

LL _pow(LL a, LL k) {
	LL res = 1;
	while (k) {
		if (k&1) res = (res * a) % MOD;
		a = (a * a) % MOD;
		k >>= 1;
	}
	return res;
}

int main() {
	ios::sync_with_stdio(0);
	cin.tie(0);

	LL N, K;
	cin >> N >> K;

	LL res = (_pow(K, (N+1)/2) - K) % MOD;
	res = (res * (N/2)) % MOD;
	res = (res + K) % MOD;
	cout << res << endl;

	return 0;
}