Rotated Palindromes

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

inputFormat

Input

The input is given from Standard Input in the following format:

N K

outputFormat

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

样例

1000000000 1000000000

875699961