Problem: 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.

Constraints

* $1 \leq n \leq 28$
* $0 \leq k \leq 18$
* $k \leq n$
* $0 \leq b_i < n$

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.

Example

Input

4
2 0 2


Output

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

Solution (in CPP):

Solution:
#include<bits/stdc++.h>
typedef long long int ll;
typedef unsigned long long int ull;
#define BIG_NUM 2000000000
#define HUGE_NUM 1000000000000000000
#define MOD 1000000007
#define EPS 0.000000001
using namespace std;



struct Info{
	Info(int arg_sum,int arg_state){
		sum = arg_sum;
		state = arg_state;
	}
	bool operator<(const struct Info &arg) const{

		return sum < arg.sum;
	}
	int sum,state;
};

int N;
int POW[30];
vector<Info> info;

int main(){

	POW[0] = 1;
	for(int i = 1; i < 30; i++){

		POW[i] = POW[i-1]*2;
	}

	scanf("%d",&N);

	int num;
	scanf("%d",&num);

	int tmp;
	vector<int> V;

	for(int i = 0; i < num; i++){

		scanf("%d",&tmp);
		V.push_back(tmp);
	}

	sort(V.begin(),V.end());

	for(int state = 0; state < POW[V.size()]; state++){
		int sum = 0;
		for(int i = 0; i < V.size(); i++){
			if(state & POW[i]){

				sum += POW[V[i]];
			}
		}
		info.push_back(Info(sum,state));
	}

	for(int i = 0; i < info.size(); i++){

		printf("%d:",info[i].sum);
		for(int k = 0; k < V.size(); k++){
			if((info[i].state&POW[k])){
				printf(" %d",V[k]);
			}
		}
		printf("\n");
	}

	return 0;
}