Quantity of Strings

2000ms

262144K

Description:

Just in case somebody missed it: this winter is totally cold in Nvodsk! It is so cold that one gets funny thoughts. For example, let's say there are strings with the length exactly n, based on the alphabet of size m. Any its substring with length equal to k is a palindrome. How many such strings exist? Your task is to find their quantity modulo 1000000007 (10⁹ + 7). Be careful and don't miss a string or two!

Let us remind you that a string is a palindrome if it can be read the same way in either direction, from the left to the right and from the right to the left.

Input:

The first and only line contains three integers: n, m and k (1 ≤ n, m, k ≤ 2000).

Output:

Print a single integer — the number of strings of the described type modulo 1000000007 (10⁹ + 7).

Sample Input:

1 1 1

Sample Output:

Sample Input:

5 2 4

Sample Output:

Note:

In the first sample only one string is valid: "a" (let's denote the only letter of our alphabet as "a").

In the second sample (if we denote the alphabet letters as "a" and "b") the following strings are valid: "aaaaa" and "bbbbb".

Informação

Provedor Codeforces

Código CF150B