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 <iostream>
#include <vector>
using namespace std;

int main() {
    int n,k;
    unsigned int bitNum = 0,maxNum = 0;
    cin >> n >> k;
    vector<int> vec(k),vec2;
    for(int i = 0;i < k;++i){
        cin >> vec[i];
        maxNum |= 1 << vec[i];
    }
    
    if(vec.size() == 0){
        cout << "0:" << endl;
        return 0;
    }
   
    for(int i = 0;i < (1 << n);++i){
        if(i > maxNum){
            return 0;
        }
        for(int j = 0;j < vec.size();++j){
            int bit = 1 << vec[j];
            if(i & bit){
                bitNum |= bit;
                vec2.push_back(vec[j]);
                if(bitNum == i){
                    j = vec.size();
                }
            }
        }
        if(bitNum == i){
            cout << i << ":";
            for(int j = 0;j < vec2.size();++j){
                cout << " " << vec2[j];
            }
            cout << endl;
        }
        vec2.clear();
        bitNum = 0;
    }
}