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:

import itertools

n = int(input())
tlist = list(map(int, input().split()))
k = tlist[0]
tlist.remove(tlist[0])

if k == 0:
    print("0:")
    exit()

combslist = []
for i in range(1, k+1):
    combs = list(itertools.combinations(tlist, i))
    for comb in combs:
        combslist.append(comb)

sumlist = []
for comb in combslist:
    sum = 0
    for c in comb:
        sum += pow(2, c)
    sumlist.append(sum)

z = zip(sumlist, combslist)
z = sorted(z)

sumlist, combslist = zip(*z)

print("0:")
for sum, comb in zip(sumlist, combslist):
    c_str = (' '.join(str(c) for c in comb))
    print(str(sum) + ": " + c_str)