Time Limit: 2000/1000 MS (Java/Others)
Memory Limit: 65536/32768 K (Java/Others)
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.
Zhejiang Provincial Programming Contest 200