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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;

class Procon {
  public Procon () { }
  static void Main (string[] agrs) {
    new Procon ().Do ();
  }

  Scanner cin;

  public void Do () {
    int[] costs = new int[9] { 2, 5, 5, 4, 5, 6, 3, 7, 6 };
    cin = new Scanner ();
    int N = cin.nextInt ();
    int M = cin.nextInt ();
    List<int> A = new List<int> (cin.arrayInt ());

    int[] DP = new int[N + 1];
    for (int i = 0; i < N; i++) {
      DP[i] = -1;
    }

    DP[0] = 0;
    for (int i = 0; i <= N; i++) {
      for (int j = 0; j < A.Count (); j++) {
        if (i - costs[A[j] - 1] < 0) {
          continue;
        }
        int tmp = DP[i - costs[A[j] - 1]] + 1;
        if (tmp > DP[i]) {
          DP[i] = tmp;
        }
      }
    }

    int maxlen = DP[N];
    int tmpN = N;
    A.Sort ((a, b) => a - b);
    for (int i = maxlen; i > 0; i--) {
      for (int j = A.Count () - 1; j >= 0; j--) {
        if (tmpN - costs[A[j] - 1] < 0) {
          continue;
        }
        if (DP[tmpN - costs[A[j] - 1]] + 1 == DP[tmpN]) {
          tmpN = tmpN - costs[A[j] - 1];
          Console.Write (A[j]);
          break;
        }
      }
    }
  }
}

class Scanner {
  string[] s;
  int i;
  int max_i;

  public Scanner () {
    s = new string[0];
    max_i = 0;
    i = 0;
  }

  public string nextString () {
    if (i >= s.Length) {
      s = Console.ReadLine ().Split (' ');
      max_i = s.Length;
      i = 0;
      if (max_i == 0) {
        return "";
      }
      return s[i++];
    } else {
      return s[i++];
    }
  }

  public int nextInt () {
    return int.Parse (nextString ());
  }

  public long nextLong () {
    return long.Parse (nextString ());
  }

  public double nextDouble () {
    return double.Parse (nextString ());
  }

  public string[] arrayString () {
    return Console.ReadLine ().Split (' ');
  }

  public int[] arrayInt () {
    string[] str = Console.ReadLine ().Split (' ');
    int[] array = new int[str.Length];
    for (int i = 0; i < str.Length; i++) {
      array[i] = int.Parse (str[i]);
    }
    return array;
  }

  public long[] arrayLong () {
    string[] str = Console.ReadLine ().Split (' ');
    long[] array = new long[str.Length];
    for (int i = 0; i < str.Length; i++) {
      array[i] = long.Parse (str[i]);
    }
    return array;
  }

  public double[] arrayDouble () {
    string[] str = Console.ReadLine ().Split (' ');
    double[] array = new double[str.Length];
    for (int i = 0; i < str.Length; i++) {
      array[i] = double.Parse (str[i]);
    }
    return array;
  }
}