Contest Duration: - (local time) (100 minutes) Back to Home
F - Rotated Palindromes /

Time Limit: 2 sec / Memory Limit: 256 MB

問題文

まず、高橋君が次の条件をすべて満たす数列 a を用意します。

• a は長さ N である。
• a の各要素は 1 以上 K 以下の整数である。
• a は回文である。 すなわち、a を逆順にした数列は元の a と一致する。

• a の先頭要素を末尾へ移動する。

• 1≤N≤10^9
• 1≤K≤10^9

入力

N K


入力例 1

4 2


出力例 1

6


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

入力例 2

1 10


出力例 2

10


入力例 3

6 3


出力例 3

75


入力例 4

1000000000 1000000000


出力例 4

875699961


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?

• 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