Score : $800$ points

Problem Statement

You are given an integer sequence of length $N$: $A=(A_1,A_2,\dots,A_N)$.

Find the $K$ smallest positive integers $X$ that satisfy the following condition.

• There is no non-empty (not necessarily contiguous) subsequence of $A$ whose elements sum to $X$.

Constraints

• $1 \leq N \leq 60$
• $1 \leq K \leq 1000$
• $1 \leq A_i \leq 10^{15}$
• All input values are integers.

Input

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

$N$ $K$

$A_1$ $A_2$ $\dots$ $A_N$

Output

Print the $K$ smallest positive integers satisfying the conditions in ascending order, separated by spaces.

3 3
1 2 5

4 9 10

The subsequences of $A$ are $(1),(2),(1,2),(5),(1,5),(2,5),(1,2,5)$, and their respective sums are $1,2,3,5,6,7,8$. Therefore, for $X=1,2,3,5,6,7,8$, there are subsequences of $A$ whose elements sum to $X$.

On the other hand, for $X=4,9,10$, there is no subsequence of $A$ whose elements sum to $X$.

20 10
324 60 1 15 60 15 1 60 319 1 327 1 2 60 2 345 1 2 2 15

14 29 44 59 74 89 104 119 134 149