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.util.HashSet;
import java.util.Scanner;
import java.util.Set;
import java.util.TreeMap;

public class Main {
	static int[] honsuu = {0, 2, 5, 5, 4, 5, 6, 3, 7, 6};
	static int[][] bou = {
			{1, 2},
			{7, 3},
			{4, 4},
			{5, 5},
			{3, 5},
			{2, 5},
			{9, 6},
			{6, 6},
			{8, 7}
			};

	public static void main(String[] args) throws Exception {
		// 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();
		Set<Integer> aSet = new HashSet<Integer>();
		for (int i = 0; i < m; i++) {
			Integer ai = sc.nextInt();
			aSet.add(ai);
			honsuuMap.put(honsuu[ai], 0);
		}
		sc.close();

		// 各桁の数字配列（使用本数の少ない順）
		Integer[] array = honsuuMap.keySet().toArray(new Integer[0]);

		editHonsuuMap(n, array, 0, honsuuMap);
//		for (Entry<Integer, Integer> entry : honsuuMap.entrySet()) {
//			System.out.print(entry.getKey() + " " + entry.getValue());
//			System.out.println();
//		}

		int totalKetasuu = 0;
		for (int val : honsuuMap.values()) {
			totalKetasuu += val;
		}

		int[] ketasuuArray = new int[10];
		editKetasuuArray(n, totalKetasuu, aSet, 9, honsuuMap, ketasuuArray);
//		for (int val : ketasuuArray) {
//			System.out.print(val + " ");
//		}
//		System.out.println();

		for (int i = 9; i >= 1; i--) {
			for (int j = 0; j < ketasuuArray[i]; j++) {
				System.out.print(i);
			}
		}
		System.out.println();
	}

	/**
	 * 合計桁数が最大になるように本数の内訳を設定
	 */
	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;
	}

	/**
	 * 決まった合計桁数の中で、より大きい値の桁数が最多になるように本数の内訳を設定
	 */
	private static boolean editKetasuuArray(
			int n, int totalKetasuu, Set<Integer> aSet, int startVal, TreeMap<Integer, Integer> honsuuMap,
			int[] ketasuuArray) {
		for (int i = startVal; i >= 0; i--) {
			if (!aSet.contains(i)) {
				continue;
			}
			if (honsuu[i] * totalKetasuu == n) {
				ketasuuArray[i] += totalKetasuu;
				return true;
			}

			int zanHonsuu = n - honsuu[i];
			int zanKetasuu = totalKetasuu - 1;
			if (zanHonsuu < 0 || zanKetasuu < 0
					|| zanKetasuu * honsuuMap.lastKey() < zanHonsuu
					|| zanHonsuu < zanKetasuu * honsuuMap.firstKey()) {
				continue;
			}

			boolean flg = editKetasuuArray(zanHonsuu, zanKetasuu, aSet, i, honsuuMap, ketasuuArray);
			if (flg) {
				ketasuuArray[i]++;
				return true;
			}
		}
		return false;
	}
}