CF14E.Camels
普及/提高-
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题目描述
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 (x1,y1) , (x2,y2) , ..., (xn,yn) . The first vertex has a coordinate x1=1 , the second — x2=2 , etc. Coordinates yi 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 yi 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 .
输入格式
The first line contains a pair of integers n and t ( 3<=n<=20 , 1<=t<=10 ).
输出格式
Output the required amount of camels with t humps.
输入输出样例
输入#1
6 1
输出#1
6
输入#2
4 2
输出#2
0
说明/提示
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 yi ).