Rhythm Logic

A drummer is composing a pattern of length N. Each beat can be a Rest (0), a Snare (1), or a Kick (2). The pattern must follow these rules: 1. No more than two Rests (0) can occur consecutively. 2. A Kick (2) can never be followed immediately by another Kick. 3. The total number of Snares (1) in the entire pattern must be exactly K. Read N and K from stdin. Output the total number of valid patterns. Example: Input: 3 1 Output: 9 (Valid: [0,1,0], [0,1,2], [1,0,0], [1,0,2], [1,2,0], [0,0,1], [2,1,0], [2,1,2], [2,0,1])