Problem Statement

There are $10^{100}$ cookies of each of $N$ types. The deliciousness per cookie of the $i$-th type is $A_i$.

You will choose a total of $K$ cookies from these. Two ways of choosing cookies are considered the same if and only if the multisets of types of chosen cookies match.

For each of the $\binom{N+K-1}{K}$ ways of choosing, consider the sum of deliciousness of the chosen cookies. Let $S_1,S_2,\dots$ be these sums in descending order, with duplicates included. Find $S_1,\dots,S_X$.

Constraints

• $1\leq N \leq 50$
• $1 \leq K \leq 10^5$
• $1 \leq X \leq \min\left(10^5, \binom{N+K-1}{K}\right)$
• $-10^9 \leq A_i \leq 10^9$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

N K X
A_1 \dots A_N

Output

Let $S_1,S_2,\dots$ be the possible sums of deliciousness of the chosen $K$ cookies in descending order, with duplicates included. Output $S_1,\dots,S_X$ in this order, separated by newlines.