Time Limit: Java: 2000 ms / Others: 2000 ms
Memory Limit: Java: 65536 KB / Others: 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].