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ZOJ Problem Set - 2745
01-K Code

Time Limit: 2 Seconds      Memory Limit: 65536 KB

Consider a code string S of N symbols, each symbol can only be 0 or 1. In any consecutive substring of S, the number of 0's differs from the number of 1's by at most K. How many such valid code strings S are there?

For example, when N is 4, and K is 3, there are two invalid codes: 0000 and 1111.


The input consists of several test cases. For each case, there are two positive integers N and K in a line.

N is in the range of [1, 62].

K is in the range of [2, 5].


Output the number of valid code strings in a line for each case.

Sample Input

1 2
4 3

Sample Output


Author: ZHENG, Jianqiang
Source: Zhejiang Provincial Programming Contest 2006
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