A number is called nillless if it is integer and positive and contains no zeros. You can make a positive integer nillless by simply omitting the zeros. We denote this with square brackets, for example $[2050] = 25$ and $[13] = 13$. When we multiply, add, and subtract we indicate with square brackets when we omit the zeros. For example, $[[4 \cdot 5] + 7] = [[20] + 7] = [2 + 7] = [9] = 9$ and $[[5 + 5] + 9] = [[10] + 9] = [1 + 9] = [10] = 1$. The following is known about the two numbers $a$ and $b$: $\bullet$ $a$ and $b$ are nillless, $\bullet$ $1 < a < b < 100$, $\bullet$ $[[a \cdot b] - 1] = 1$. Which pairs $(a, b)$ satisfy these three requirements?