
54  ZJPCPC Sunny Cup 2006, Online Round  1004
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. Input 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 Output the number of valid code strings in a line for each case. Sample Input 1 2 4 3 Sample Output 2 14 Author: ZHENG, Jianqiang 