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;

int main() {
    ll n; cin >> n;
    ll k; cin >> k;
    ll A=0;
    vector<ll> b(k);
    for(ll i=0; i<k; i++){
        cin >> b[i];
        A |= (1<<b[i]);
    }
    vector<ll> sb;
    for(ll bit=A; ; bit = (bit-1)&A){
        sb.push_back(bit);
        
        if(!bit) break;
    }
    sort(sb.begin(),sb.end());
    
    for(int i=0; i<sb.size(); i++){
        cout << sb[i] <<":";
        for(int j=0; j<n; j++){
            if(sb[i] & (1<<j)){
                cout <<" "<< j;
            }
        }
        cout << endl;
    }

}