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

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