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: Time Limit Exceeded)

import java.util.*;

public class Main {
  private static final int[] mnum = { 0, 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 i = 0; i < M; i++) {
      A[i] = sc.nextInt();
    }
    Arrays.sort(A);
    
    int[] dp = new int[N+1];
    for (int i = 1; i <= N; i++) {
      for (int j = 0; j < M; j++) {
        if (i - mnum[A[j]] >= 0) {
          dp[i] = Math.max(dp[i], dp[i-mnum[A[j]]]+1);
        }
      }
    }
    
    String ans = "";
    int remain = dp[N];
    int match = N;
    while (match > 0) {
      for (int j = M-1; j >= 0; j--) {
        if (match-mnum[A[j]] < 0) {
          continue;
        }
        if (remain == 1) {
          if (match-mnum[A[j]] == 0) {
            ans = ans + Integer.toString(A[j]);
            match -= mnum[A[j]];
            break;
          }
        } else {
          if (dp[match-mnum[A[j]]] == remain-1) {
            ans = ans + Integer.toString(A[j]);
            match -= mnum[A[j]];
            remain--;
            break;
          }
        }
      }
    }
    
    System.out.println(ans);
  }
}