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

• $1 \leq N \leq 10^9$
• $1 \leq K \leq 10^9$

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 $10^9+7$.

4 2

6

The following six sequences can be obtained:

• $(1, 1, 1, 1)$
• $(1, 1, 2, 2)$
• $(1, 2, 2, 1)$
• $(2, 2, 1, 1)$
• $(2, 1, 1, 2)$
• $(2, 2, 2, 2)$

1 10

10

6 3

75

1000000000 1000000000

875699961