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;

int main(){
  cin.tie(0);
 	ios::sync_with_stdio(false);
  int n, k;
  cin >> n >> k;
  int b[k];
  for(int i = 0; i < k; i++){
    cin >> b[i];
  }
  for(int i = 0; i < (1 << k); i++){
    bitset<28> a(i);

    bitset<28> t(0);
    bool flag = true;
    for(int j = 0; j < 28; j++){
      if(flag){
        if(a[j]){
          t = (1 << b[j]);
          flag = false;
        }
      }else{
        if(a[j]){
          t |= (1 << b[j]);
        }
      }
    }
    cout << t.to_ulong() << ":";
    for(int j = 0; j < 28; j++){
      if(a[j]){
        cout << " " << b[j];
      }
    }
    cout << "\n";
  }
  return 0;
}