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.
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 $T$.
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.
4 2 0 2
0: 1: 0 4: 2 5: 0 2