Yet another MEX problem MEXPROB

Read problem statements in Bengali, Mandarin Chinese, Russian, and Vietnamese as well.

The MEX (minimum excluded) of an array is the smallest non-negative integer that does not belong to the array. For instance:

• The MEX of $[2, 2, 1]$ is $0$, because $0$ does not belong to the array.
• The MEX of $[3, 1, 0, 1]$ is $2$, because $0$ and $1$ belong to the array, but $2$ does not.
• The MEX of $[0, 3, 1, 2]$ is $4$, because $0, 1, 2$ and $3$ belong to the array, but $4$ does not.

You are given an array $A$ of length $N$. You create a list $B$ consisting of the MEX-es of all subarrays of the array $A$. Formally, for all pairs $(l, r)$ such that $1 \leq l \leq r \leq N$, you calculate $MEX(A_l, A_{l + 1}, \dots, A_r)$ and append the value in the list $B$. Find the $K$-th smallest value in the list $B$.

Note: Since the size of the input and output is large, please use fast input-output methods.