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:
#!/usr/bin/env python3
# ITP2_11_C: Bitset 2 - Enumeration of Subsets 3

from functools import lru_cache


def subset(n, mask):
    @lru_cache(maxsize=None)
    def _subset(i):
        if i < 0:
            return [(0, [])]
        m = mask[i]
        return (_subset(i-1) +
                [(v + (1 << m), vs + [m]) for v, vs in _subset(i-1)])

    return _subset(len(mask)-1)


def run():
    n = int(input())
    mask = tuple([int(i) for i in input().split()][1:])

    for i, vs in subset(n, mask):
        print("{}:{}".format(i, "".join([" {}".format(v) for v in vs])))


if __name__ == '__main__':
    run()