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: Accepted)

import java.io.*;
import java.util.*;
import java.util.function.*;

class Pair {
	int a, b;

	Pair(int a, int b) {
		this.a = a;
		this.b = b;
	}
}

final class Solver {
	static final Solver INSTANCE = new Solver();

	void solve(Supplier<String> sc) {
		int N = Integer.parseInt(sc.get());
		int M = Integer.parseInt(sc.get());
		int[] A = new int[M];
		Arrays.setAll(A, $ -> Integer.parseInt(sc.get()));
		int[] num = {-1, 2, 5, 5, 4, 5, 6, 3, 7, 6};
		Pair[] usable = new Pair[M];
		for (int i = 0; i < M; i++) {
			usable[i] = new Pair(A[i], num[A[i]]);
		}
		Arrays.sort(usable, Comparator.comparingInt((Pair p) -> p.b).thenComparingInt(p -> p.a));
		TreeMap<Integer, Integer> higher = new TreeMap<>();
		for (Pair pair : usable) {
			higher.put(pair.b, pair.a);
		}

		final String INF = String.valueOf((char) 0);
		String[] maxNum = new String[N + 1];
		Arrays.fill(maxNum, INF);
		maxNum[0] = "";
		for (int i = 2; i <= N; i++) {

			for (Map.Entry<Integer, Integer> entry = higher.floorEntry(i);
				 entry != null;
				 entry = higher.lowerEntry(entry.getKey())) {
				String base = maxNum[i - entry.getKey()];
				if (base == INF) continue;
				String candidate = base + entry.getValue();
				if (numeroComp.compare(maxNum[i], candidate) > 0) maxNum[i] = candidate;
			}
		}
		System.out.println(maxNum[N]);
	}

	Comparator<String> numeroComp = Comparator.comparingInt(String::length).thenComparing(s -> s).reversed();
}

class Main {
	public static void main(String... args) {
		System.setOut(new PrintStream(new BufferedOutputStream(System.out)));
		BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
		Solver.INSTANCE.solve(new Supplier<String>() {
			StringTokenizer line;

			public String get() {
				try {
					return (line = line != null && line.hasMoreTokens() ? line : new StringTokenizer(reader.readLine())).nextToken();
				} catch (IOException e) {
					throw new UncheckedIOException(e);
				}
			}
		});
		System.out.flush();
	}
}