Problem:
Score : 400 points

Problem Statement

Find the largest integer that can be formed with exactly N matchsticks, under the following conditions:

Every digit in the integer must be one of the digits A_1, A_2, ..., A_M (1 \leq A_i \leq 9).

The number of matchsticks used to form digits 1, 2, 3, 4, 5, 6, 7, 8, 9 should be 2, 5, 5, 4, 5, 6, 3, 7, 6, respectively.

Constraints

All values in input are integers.

2 \leq N \leq 10^4

1 \leq M \leq 9

1 \leq A_i \leq 9

A_i are all different.

There exists an integer that can be formed by exactly N matchsticks under the conditions.

Input

Input is given from Standard Input in the following format:

N M
A_1 A_2 ... A_M

Output

Print the largest integer that can be formed with exactly N matchsticks under the conditions in the problem statement.

Sample Input 1

20 4
3 7 8 4

Sample Output 1

777773

The integer 777773 can be formed with 3 + 3 + 3 + 3 + 3 + 5 = 20 matchsticks, and this is the largest integer that can be formed by 20 matchsticks under the conditions.

Sample Input 2

101 9
9 8 7 6 5 4 3 2 1

Sample Output 2

71111111111111111111111111111111111111111111111111

The output may not fit into a 64-bit integer type.

Sample Input 3

15 3
5 4 6

Sample Output 3

654

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Collections;
import java.util.Deque;
import java.util.HashMap;
import java.util.HashSet;
import java.util.List;
import java.util.Map;
import java.util.Scanner;
import java.util.Set;
import java.util.concurrent.LinkedBlockingDeque;

public class Main {
	int N, M;
	Set<Integer> A;
	Map<Integer, Integer> cost;
	int[] baseCost = { 2, 5, 5, 4, 5, 6, 3, 7, 6 };
	int[] baseOrder = { 1, 7, 4, 5, 3, 2, 9, 6, 8 };
	List<Integer> searchOrder;
	Deque<Integer> result;

	Main() {
		Scanner in = new Scanner(System.in);
		String[] tokens = in.nextLine().split(" ");
		N = Integer.parseInt(tokens[0]);
		M = Integer.parseInt(tokens[1]);
		A = new HashSet<>();
		tokens = in.nextLine().split(" ");
		cost = new HashMap<>();
		searchOrder = new ArrayList<>();
		for (int i = 0; i < M; ++i) {
			int val = Integer.parseInt(tokens[i]);
			A.add(val);
		}
		for (int i = 0; i < baseOrder.length; ++i) {
			if (A.contains(baseOrder[i])) {
				searchOrder.add(baseOrder[i]);
			}
		}
		in.close();
		result = new LinkedBlockingDeque<>();
	}

	boolean search(int num) {
		if (num < 0) {
			return false;
		}
		if (num == 0) {
			return true;
		}
		if (num == 10) {
			if (A.contains(9) && A.contains(4)) {
				result.addLast(9);
				result.addLast(4);
				return true;
			}
		}
		for (int i = 0; i < searchOrder.size(); ++i) {
			int val = searchOrder.get(i);
			result.addLast(val);
			boolean r = search(num - baseCost[val - 1]);
			if (r) {
				return true;
			} else {
				result.pollLast();
			}
		}
		return false;
	}

	void calc() {
		search(N);
	}

	void show() {
		List<Integer> list = new ArrayList<>(result.size());
		list.addAll(result);
		Collections.sort(list);
		Collections.reverse(list);
		for (int i = 0; i + 1 < list.size(); ++i) {
			System.out.print(list.get(i));
		}
		System.out.println(list.get(list.size() - 1));
	}

	public static void main(String[] args) {
		Main ins = new Main();
		ins.calc();
		ins.show();
	}

}