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.ArrayList;
import java.util.Collections;
import java.util.List;
import java.util.Scanner;
 
public class Main {
  public static void main(String[] args) {
    Scanner scanner = new Scanner(System.in);
 
    // N matchsticks
    int N = scanner.nextInt();
    // M: Every digit in the integer must be one of the digits A1~AM
    int M = scanner.nextInt();
    int[] a = new int[M];
    for (int i = 0; i < M; i++)
    {
      a[i] = scanner.nextInt();
    }
      
    int[] cost = new int[] {0, 2, 5, 5, 4, 5, 6, 3, 7, 6};
    int[] dp = new int[N + 1];
    
    // dp[1]~dp[N] = -1
    for (int i = 1; i <= N; i++) 
    {
      dp[i] = -1;
    }
    
    // Trace from the a[i] with smallest cost
    for (int i = 1; i <= N; i++)
    {  
      for (int j = 0; j < M; j++)
      {  
        if (i >= cost[a[j]]) 
          dp[i] = Math.max(dp[i], dp[i - cost[a[j]]] + 1);
      }
    }
    int k = dp[N];
    List<Integer> list = new ArrayList<>();


    for (int i = 0; i < k; i++) 
    {
      int d = 0;
      for (int j = 0; j < M; j++)
      {
        if (N >= cost[a[j]] && dp[N] == dp[N - cost[a[j]]] + 1)
        {
          d = Math.max(d, a[j]);
        }
      }
      list.add(d);
      N -= cost[d];
    }
    Collections.sort(list);
    StringBuilder sb = new StringBuilder();
    for (int i = list.size() - 1; i >= 0; i--) 
    {
      sb.append(list.get(i));
    }
    System.out.println(sb.toString());
  }
}