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5 초 256 MB 14 2 2 14.286%

문제

Once upon a time, there was a school canteen. And the cooks were very busy there. They had to prepare a menu for all n days of the school year, but they had to admit that they are able to make only k different meals.

Alas, the students are known to be picky eaters. (Which is a well established Czech tradition.) If they get the same meal for ℓ days consecutively, they rebel against the cooks. (defenestration, which is another fine Czech tradition.)

Count the number of menus, which avoid student rebellion.

입력

On the standard input, you will find a single line containing three space-separated integers: n, ℓ, and k. Here n is the number of days (0 ≤ n ≤ 2,000,000,000), ℓ the impatience of the students (the number of repeats of a single meal, which causes the students to rebel, 2 ≤ ℓ ≤ 200), and k is the number of possible meals (1 ≤ k ≤ 100).

 

출력

The standard output shall contain a single integer: the number of possible menus modulo 4,000,000,009.

예제 입력

3 2 3

예제 출력

12

힌트

There are exactly 12 menus of the required properties:

1 2 1
1 2 3
1 3 1
1 3 2
2 1 2
2 1 3
2 3 1
2 3 2
3 1 2
3 1 3
3 2 1