A7762. Camels

Bob likes to draw camels: with a single hump, two humps, three humps, etc. He draws a camel by connecting points on a coordinate plane. Now he's drawing camels with $t$ humps, representing them as polylines in the plane. Each polyline consists of $n$ vertices with coordinates $(x_{1},y_{1})$ , $(x_{2},y_{2})$ , ..., $(x_{n},y_{n})$ . The first vertex has a coordinate $x_{1}=1$ , the second — $x_{2}=2$ , etc. Coordinates $y_{i}$ might be any, but should satisfy the following conditions:

- there should be $t$ humps precisely, i.e. such indexes $j$ ( $2<=j<=n-1$ ), so that $y_{j-1}<y_{j}>y_{j+1}$ ,
- there should be precisely $t-1$ such indexes $j$ ( $2<=j<=n-1$ ), so that $y_{j-1}>y_{j}<y_{j+1}$ ,
- no segment of a polyline should be parallel to the $Ox$ -axis,
- all $y_{i}$ are integers between 1 and 4.

For a series of his drawings of camels with $t$ humps Bob wants to buy a notebook, but he doesn't know how many pages he will need. Output the amount of different polylines that can be drawn to represent camels with $t$ humps for a given number $n$ .

The first line contains a pair of integers $n$ and $t$ ( $3<=n<=20$ , $1<=t<=10$ ).

Output the required amount of camels with $t$ humps.

In the first sample test sequences of $y$ -coordinates for six camels are: 123421, 123431, 123432, 124321, 134321 и 234321 (each digit corresponds to one value of $y_{i}$ ).