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.*;

public class Main {

    private static final int[] NS = new int[]{2, 5, 5, 4, 5, 6, 3, 7, 6};

    public static void main(String[] args) {

        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        int M = sc.nextInt();
        int[] A = new int[M];
        for (int m = 0; m < M; m += 1) {
            A[m] = sc.nextInt();
        }

        int[] dp = new int[N + 1];
        dp[0] = 0;
        for (int n = 1; n <= N; n += 1) {
            int next = -1;
            for (int a : A) {
                int prevDP = n - NS[a - 1];
                if (prevDP < 0) {
                    continue;
                }
                int curNext = dp[prevDP] + 1;
                if (next < curNext) {
                    next = curNext;
                }
            }
            dp[n] = next;
        }

        String integer = "";
        int curN = N;
        for (int n = 0; n < dp[N]; n += 1) {
            int curA = 0;
            for (int a : A) {
                int nextDP = curN - NS[a - 1];
                if (curA < a && nextDP >= 0) {
                    if (dp[nextDP] == (dp[curN] - 1)) {
                        curA = a;
                    }
                }
            }
            curN = curN - NS[curA - 1];
            integer += curA;
        }

        System.out.println(integer);

    }

}