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;
#define rep(i,n) for(int i=0; i<(n); i++)
#define FOR(i,x,n) for(int i=x; i<(n); i++)
#define ALL(n) begin(n),end(n)
#define MOD 1000000007
 
typedef long long ll;
typedef unsigned int ui;
typedef unsigned long long ull;
template <class T>
void print(T& x){printf("%d\n", x);}

ll N, K, X;

void printnum(ll i, ll n){
    ll bit;
    printf("%lld:", i);
    for(ll j=0; j<n; j++){
        if(i&(1<<j)) printf(" %d", j);
    }
    printf("\n");
}

void iter(ll x, ll bit){
    // cout << "x=" << x << ", bit=" << bit << endl;
    // cout << bitset<32>(x) << endl;
    // cout << bitset<32>(1<<bit) << endl;
    // cout << bitset<32>(X) << endl;
    if(bit<0){
        printnum(x, N);
        return;
    }
    // printf("%d\n", X & (1<<bit));
    // if((X & (1<<bit))==0) {
    //     printf("returned\n");
    //     return;
    // }
    //unuse
    iter(x, bit-1);

    // use
    if((X & (1<<bit))!=0) {
        iter(x|(1<<bit), bit-1);
    }
    
}
 
int main()
{
    cin >> N;
    cin >> K;
    ll tmp;
    rep(i, K){
        cin >> tmp;
        X |= (1 << tmp);
    }

    iter(0, N);

    return 0;
}