Enumeration of Subsets II
You are given a set T, which is a subset of U. The set U consists of 0, 1, ... n-1. Print all sets, each of which is a subset of U and includes T as a subset. 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.
nn kb0b1...bk−1kb0b1...bk−1
kk is the number of elements in TT, and bibi represents elements in TT.
Output
Print the subsets ordered by their decimal integers. Print a subset in the following format.
dd: e0e0 e1e1 ...
Print ':' after the integer value dd, then print elements eiei in the subset in ascending order. Separate two adjacency elements by a space character.