49*. On the board, there are 128 ones. In one move, you can replace a pair of numbers $a$ and $b$ with the number $a b + 1$. Let $A$ be the maximum number that can appear on the board after 127 such operations. What is its last digit?

## 11th grade
92.49. Hint. Prove that to obtain the maximum number, you can act according to the following scheme: at each moment, perform the operation on the two smallest numbers.

By now, carrying out the calculations in accordance with the derived algorithm, we get that the last digit of the maximum number is two.