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 <algorithm>
#include <vector>
#include <string>
#define int long long
using namespace std;
int n, a[20], l[20], k;
bool b[20];
void f(int i) {
	if (i < 0) {
		int r = 0;
		for (int p = 0; p < k; p++) if (b[p]) r += a[p];
		cout << r << ':';
		for (int p = 0; p < k; p++)if (b[p])cout << ' ' << l[p];
		cout << endl;
		return;
	}
	b[i] = 0;
	f(i - 1);
	b[i] = 1;
	f(i - 1);
	return;
}
signed main() {
	cin >> n >> k;
	for (int i = 0; i < k; i++) {
		a[i] = 1;
		cin >> l[i];
		for (int j = 0; j < l[i]; j++)a[i] *= 2;
	}
	sort(a, a + k);
	f(k - 1);
}