Problem:
Enumeration of Subsets III

You are given a set $T$, which is a subset of $S$. The set $S$ consists of $0, 1, ... n-1$.

Print all subsets of $T$.

Note that we represent $0, 1, ... n-1$ as 00...0001, 00...0010, 00...0100, ..., 10...0000 in binary respectively and the integer representation of a subset is calculated by bitwise OR of existing elements.

Input

The input is given in the following format.

$n$
$k \; b_0 \; b_1 \; ... \; b_{k-1}$

$k$ is the number of elements in $T$, and $b_i$ represents elements in $T$.

Output

Print the subsets ordered by their decimal integers. Print a subset in the following format.

$d$: $e_0$ $e_1$ ...

Print ':' after the integer value $d$, then print elements $e_i$ in the subset in ascending order. Separate two adjacency elements by a space character.

Constraints

$1 \leq n \leq 28$

$0 \leq k \leq 18$

$k \leq n$

$0 \leq b_i < n$

Sample Input 1

4
2 0 2

Sample Output 1

0:
1: 0
4: 2
5: 0 2

Solution in Ruby (judge verdict: Accepted)

h={};n=gets.to_i;a=gets.split.map(&:to_i)[1..-1]
(1<<a.size).times{|i|x=0;y=[];a.size.times{|j|i[j]>0&&(x+=1<<a[j];y<<a[j])};h[x]=y}
puts h.sort.map{|k,v|k.to_s+':'+v.map{|e|' %d'%e}*''}