Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

D. Wall Bars

time limit per test

4 secondsmemory limit per test

512 megabytesinput

standard inputoutput

standard outputManao is working for a construction company. Recently, an order came to build wall bars in a children's park. Manao was commissioned to develop a plan of construction, which will enable the company to save the most money.

After reviewing the formal specifications for the wall bars, Manao discovered a number of controversial requirements and decided to treat them to the company's advantage. His resulting design can be described as follows:

- Let's introduce some unit of length. The construction center is a pole of height
*n*. - At heights 1, 2, ...,
*n*exactly one horizontal bar sticks out from the pole. Each bar sticks in one of four pre-fixed directions. - A child can move from one bar to another if the distance between them does not exceed
*h*and they stick in the same direction. If a child is on the ground, he can climb onto any of the bars at height between 1 and*h*. In Manao's construction a child should be able to reach at least one of the bars at heights*n*-*h*+ 1,*n*-*h*+ 2, ...,*n*if he begins at the ground.

Manao is wondering how many distinct construction designs that satisfy his requirements exist. As this number can be rather large, print the remainder after dividing it by 1000000009 (10^{9} + 9). Two designs are considered distinct if there is such height *i*, that the bars on the height *i* in these designs don't stick out in the same direction.

Input

A single line contains two space-separated integers, *n* and *h* (1 ≤ *n* ≤ 1000, 1 ≤ *h* ≤ *min*(*n*, 30)).

Output

In a single line print the remainder after dividing the number of designs by 1000000009 (10^{9} + 9).

Examples

Input

5 1

Output

4

Input

4 2

Output

148

Input

4 3

Output

256

Input

5 2

Output

376

Note

Consider several designs for *h* = 2. A design with the first bar sticked out in direction *d*_{1}, the second — in direction *d*_{2} and so on (1 ≤ *d*_{i} ≤ 4) is denoted as string *d*_{1}*d*_{2}...*d*_{n}.

Design "1231" (the first three bars are sticked out in different directions, the last one — in the same as first). A child can reach neither the bar at height 3 nor the bar at height 4.

Design "414141". A child can reach the bar at height 5. To do this, he should first climb at the first bar, then at the third and then at the fifth one. He can also reach bar at height 6 by the route second → fourth → sixth bars.

Design "123333". The child can't reach the upper two bars.

Design "323323". The bar at height 6 can be reached by the following route: first → third → fourth → sixth bars.

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Mar/22/2019 16:18:42 (d1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|