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<cmath>
#include<bitset>
using namespace std;

int main()
{
    int n, k, b;

    cin >> n;
    cin >> k;

    int u[n];
    double p = pow( 2, (double)n );
    bitset<28> s1(0);

    for( int i = 0; i < n; i++ )
        u[i] = i;

    for( int i = 0; i < k; i++ )
    {
        cin >> b;
        for( int j = 0; j < n; j++ )
        {
            if( u[j] == b )
                s1[j] = 1;
        }
    }

    for( int i = 0; i < (int)p; i++ )
    {
        bitset<28> t(i);

        bool judge = true;
        if( ( s1 | t ) != s1 )
            judge = false;

        if( judge == true )
        {
            cout << i << ":";
            for( int j = 0; j < 28; j++ )
            {
                if( t[j] == 1 )
                    cout << " " << u[j];
            }
            cout << endl;
        }
    }
    return 0;
}