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.

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.

Constraints

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

Sample Input 1

3 3
1 2 5

Sample Output 1

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.

Sample Input 2

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

Sample Output 2

14 29 44 59 74 89 104 119 134 149

见题面 Input 部分

见题面 Output 部分