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 print(bitset<32> b) {
    for (int i = 0; i < 32; i++) {
        if (b.test(i)) {
            cout << " " << i;
        }
    }
}
 
int main(void) {
    ios::sync_with_stdio(false);
    cin.tie(0);
 
    bitset<32> b1, b2;
    vector<int> vec;
 
    int n; cin >> n;
    int k; cin >> k;
    int max = 1 << k;
    for (int i = 0; i < k; i++) {
        int x; cin >> x;
        vec.push_back(x);
    }
    for (int i = 0; i < max; i++) {
        b1 = i;
        b2.reset();
        for (int j = 0; j < vec.size(); j++) {
            if (b1.test(j) == 1) {
                b2.set(vec[j]);
            }
        }
        cout << b2.to_ulong() << ":";
        print(b2);
        cout << endl;
    }
}