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 JAVA (judge verdict: Time Limit Exceeded)

import java.util.ArrayList;
import java.util.List;
import java.util.Scanner;

public class Main {
	public static void main(String[] args){
		int n, i, j = 0, pow, input = 0, k, m;
		try (Scanner sc = new Scanner(System.in)) {
			n = sc.nextInt();
			k = sc.nextInt();
			int[] a = new int[n];
			List<Integer> b = new ArrayList<>();
			for(i = 0; i < k; i++) {
				input = sc.nextInt();
				for(;j < input; j++) {
					b.add(j);
				}
				j = j + 1;
			}
			pow = (int) (Math.pow(2, j));
//			for(Integer output : b) {
//				System.out.print(output + " ");
//			}
			calculation : for(i = 0; i < pow; i++) {
				m = i;
				for(j = 0; m != 0; j++) {
					if(m % 2 == 1) {
						a[j] = 1;
						if(b.contains(j)) {
							continue calculation;
						}
					}else {
						a[j] = 0;
					}
					m /= 2;
				}
//				boolean bool = false;
//				for(j = 0; j < b.size(); j++) {
//					if(a[b.get(j)] != 0) {
//						bool = true;
//						break;
//					}
//				}
//				if(bool) continue;
				System.out.print(i + ":");
				for(j = 0; j < a.length; j++) {
					if(a[j] == 1) {
						System.out.print(" " + j);
					}
				}
				System.out.println();
			}
		}
	}
}