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 PYTHON3):

Solution:
from itertools import combinations
n = int(input())
k, *b_arr = map(int, input().split())


def calc_int(arr):
    ret = 0
    for i in arr:
        ret += 1 << i
    return ret


subsets = []
for i in range(len(b_arr)+1):
    i_subsets = []
    for sub in combinations(b_arr, i):
        i_subsets.append((calc_int(sub), sub))
    subsets.extend(i_subsets)

subsets.sort()
for sub in subsets:
    print('{}: {}'.format(sub[0], ' '.join(map(str, sub[1])))) if len(sub[1]) != 0 else print(f'{sub[0]}:')