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>
using namespace std;
typedef long long ll;
#define FOR(I,A,B) for(ll I = int(A); I < int(B); ++I)
#define SORT(x) (sort(x.begin(),x.end())) // 0 2 2 3 4 5 8 9

int main(){
	ios::sync_with_stdio(false);
	cin.tie(0);

	int n,k;
	vector<int> sk;
	cin >> n >> k;
	FOR(i,0,k){
		int x;
		cin >> x;
		sk.push_back(x);
	}
	SORT(sk);
	FOR(i,0,(1<<k)){
		int p=0;
		vector<int> s;
		FOR(j,0,k){
			if(i&(1<<j)){
				p+=(1<<sk[j]);
				s.push_back(sk[j]);
			}
		}
		cout << p << ":";
		FOR(j,0,s.size()){
			cout << " " << s[j];
		}
		cout << endl;
	}
}