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 CPP):

Solution:
#include <iostream>
#include <vector>

using ull = unsigned long long;

int main() {
    int n;
    std::cin >> n;

    int k;
    std::cin >> k;

    ull t = 0;
    for (int i = 0; i < k; ++i) {
        int b;
        std::cin >> b;
        t += (1 << b);
    }

    for (ull d = 0; d < (1 << n); ++d) {
        if (d & ~t) continue;

        std::cout << d << ":";
        for (int i = 0; i < n; ++i)
            if (d & (1 << i)) std::cout << ' ' << i;
        std::cout << std::endl;
    }
}