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;

void subsets(vector<int> U, int m) 
{
    long nSub = 1 << m;
    
    for(long i = 0; i < nSub; i++)
    {
        long d = 0;
        
        for(int k = 0; k < m; k++)
        {
            if((1 << k) & i)
            {
                d += (1 << U[k]);
            } 
        }
        
        printf("%ld:", d);
        for(int k = 0; k < m; k++)
            if((1 << k) & i)
                printf(" %d", U[k]);
        printf("\n");
    }
}

int main() 
{
    int n, m, k;
    scanf("%d %d", &n, &k);

    vector<int> U;
    
    for(int i = 0; i < k; i++)
    {
        scanf("%d", &m);
        U.emplace_back(m);
    }
    
    subsets(U, k);
    
    return 0;
}