Double or Append

You start off with initially array $A = [0]$. You need to handle $M$ operations of $2$ types: - $T_i = 1$ : Let $X = \operatorname{MEX}(A)$ $^{\dagger}$, replace $A$ with $[X] + A$. - $T_i = 2$ : Replace $A$ with $A + A$. In both the above cases, $+$ denotes array concatenation. After each operation, find the number of inversions$^{\ddagger}$ in the array $A$. It is guaranteed that the length