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 DEBUG

void enumerate_comnination(vector<int> x)
{
    ll s = 0;
    for (auto y : x)
        s += pow(2, y);
    cout << s << ":";
    for (auto y : x)
        cout << " " << y;
    cout << endl;
}

int main()
{

#ifdef DEBUG
    cout << "DEBUG MODE" << endl;
    ifstream in("input.txt"); //for debug
    cin.rdbuf(in.rdbuf());    //for debug
#endif

    int n, k, m;
    cin >> n >> k;
    int b[k];
    for (int i = 0; i < k; i++)
        cin >> b[i];

    for (int i = 0; i < pow(2, k); i++)
    {
        ll d = 0;
        int h = i;
        vector<int> x;
        for (int j = 0; j < k; j++)
        {
            if (h % 2)
            {
                x.push_back(b[j]);
                d += pow(2, b[j]);
            }
            h /= 2;
        }
        cout << d << ":";
        for (auto y : x)
            cout << " " << y;
        cout << endl;
    }
    return 0;
}