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.Arrays;
import java.util.Scanner;
import java.util.TreeMap;

public class Main {
	public static void main(String[] args) throws Exception {
		int[][] bou = {
				{1, 2},
				{7, 3},
				{4, 4},
				{5, 5},
				{3, 5},
				{2, 5},
				{9, 6},
				{6, 6},
				{8, 7}
				};
		// 1桁当たりの本数、その本数を使う桁数
		TreeMap<Integer, Integer> honsuuMap = new TreeMap<Integer, Integer>();

		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int m = sc.nextInt();
		int[] a = new int[m];
		for (int i = 0; i < m; i++) {
			a[i] = sc.nextInt();
			for (int j = 0; j < 9; j++) {
				if (a[i] == bou[j][0]) {
					honsuuMap.put(bou[j][1], 0);
					break;
				}
			}
		}
		sc.close();

		Integer[] array = honsuuMap.keySet().toArray(new Integer[0]);
		if (n % array[0] == 0) {
			// 結果出力
			return;
		}

		editHonsuuMap(n, array, 0, honsuuMap);

//		for (Entry<Integer, Integer> entry : honsuuMap.entrySet()) {
//			System.out.print(entry.getKey() + " " + entry.getValue());
//			System.out.println();
//		}

		Arrays.parallelSort(a);
		for (int i = a.length - 1; i >= 0; i--) {
			for (int j = 0; j < 9; j++) {
				if (a[i] == bou[j][0]) {
					int ketasuu = honsuuMap.get(bou[j][1]);
					for (int k = 0; k < ketasuu; k++) {
						System.out.print(a[i]);
					}
					honsuuMap.put(bou[j][1], 0);
					break;
				}
			}
		}
		System.out.println();
	}

	private static boolean editHonsuuMap(
			int n, Integer[] array, int startIdx, TreeMap<Integer, Integer> honsuuMap) {
		for (int i = startIdx; i < array.length; i++) {
			if (n % array[i] == 0) {
				honsuuMap.put(array[i], n / array[i]);
				return true;
			}

			for (int j = (n / array[i]) - 1; j >= 0; j--) {
				int tempN = n - (array[i] * j);
				boolean flg = editHonsuuMap(tempN, array, i + 1, honsuuMap);
				if (flg) {
					honsuuMap.put(array[i], j);
					return true;
				}
			}
		}
		return false;
	}
}