kex

Consider the set of non-negative integers $A$. The minimum non-negative integer that does not occur in this set is denoted $\mathrm{mex}(A)$. For example, $\mathrm{mex}(\{0, 1, 2, 4, 5, 9\})=3$.

Ann generalizes the concept of mex. For a positive integer $k$ and a set of non-negative integers $A$, $\mathrm{kex}(A,k)$ is the $k$-th smallest integer that is not in $A$. For example, $\mathrm{kex}(\{0, 1, 2, 4, 5, 9\}, 2)=6$.

For the given set $A$ and $q$ values $k_i$, find $\mathrm{kex}(A, k_i)$ for each $i$.

The first line contains two integers $n$ and $q$ ($1 \leq n, q \leq 10^5$), the number of elements in $A$ and the number of kex values to find.

The second line contains $n$ distinct non-negative integers, each at most $10^9$. These are the elements of $A$.

The third line contains $q$ integers $k_i$ ($1 \leq k_i \leq 10^9$).

Print $\mathrm{kex}(A, k_1), \mathrm{kex}(A, k_2), \ldots, \mathrm{kex}(A, k_q)$.