Question 94
The number $770$ is written on a blackboard. Melody repeatedly performs moves, where a move consists of subtracting either $40$ or $41$ from the number on the board. She performs moves until the number is not positive, and then she stops. Let $N$ be the number of sequences of moves that Melody could perform. Suppose $N = a \cdot 2^{b}$ where $a$ is an odd positive integer and $b$ is a nonnegative integer. Compute $100a + b$.