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 C (judge verdict: Accepted)

#include <stdio.h>
#define bit(n,m)(((n)>>(m))&1)

int main(){
	int n,c;
	scanf("%d%d",&n,&c);
	int s=0;
	while(c--){
		int t;
		scanf("%d",&t);
		s|=1<<t;
	}
	for(int x=0;x<1<<n;x++)if((x&s)==x){
		printf("%d:",x);
		for(int k=0;k<n;k++)if(bit(x,k))printf(" %d",k);
		puts("");
	}
}