K. The Cage in ASZoo
time limit per test
5 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

There is A huge cage in ASZoo that can contain up to $$$k$$$ animals.

There are $$$n$$$ families of animals, each of which has an infinite family members, and each kind of animal weighs $$$a_i$$$ ($$$1 \le i \le n$$$).

The zookeeper decided to put exactly $$$k$$$ animals in the cage, regardless of the kind or the weight. The zookeeper can put more than one animal of the same family in the cage, and can also discard an entire family and not putting them in the cage.

Find all possible total weights of animals that the zookeeper can put in the cage.

Input

The first line contains two integers $$$n$$$ and $$$k$$$ ($$$1 \le n, k \le 1000$$$).

The second line contains $$$n$$$ integers $$$a_1, a_2, ..., a_n$$$ ($$$1 \le a_i \le 1000$$$).

Output

Print the only line with all the possible total weights of stolen products, separated by a space. The numbers should be printed in ascending order.

Examples
Input
3 2
1 2 3
Output
2 3 4 5 6
Input
5 5
1 1 1 1 1
Output
5
Input
3 3
3 5 11
Output
9 11 13 15 17 19 21 25 27 33