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;
using ll = long long;
using ull = unsigned long long;

#define FOR(i,a,b) for(ll i=(a);i<(b);++i)
#define ALL(v) (v).begin(), (v).end()
#define p(s) cout<<(s)<<endl
#define p2(s, t) cout << (s) << " " << (t) << endl
#define br() p("")
#define pn(s) cout << (#s) << " " << (s) << endl

int main(){
    ll N;
    cin >> N;

    ll k;
    cin >> k;

    vector<ll> flags;
    FOR(i, 0, k){
        ll b; cin >> b;
        flags.push_back(b);
    }

    ll L = flags.size();
    FOR(i, 0, 1LL<<L){
        ull ma = 0;
        FOR(j, 0, L){
            if(i>>j&1){
                ll bit = flags[j];
                ma |= (1LL<<bit);
            }
        }
        cout << ma << ":";
        FOR(j, 0, 28){
            if(ma>>j&1){
                cout << ' ' << j;
            }
        }
        cout << endl;
    }
    
    return 0;
}