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: Wrong Answer)

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

class M{static void Main(string[] _) {
  var a = Console.ReadLine().Split(' ');
  var b = Console.ReadLine().Split(' ');
  var N = int.Parse(a[0]);
  var M = int.Parse(a[1]);
  
  int[] L = new int[] {0,2,5,5,4,5,6,3,7,6};
  int[] p = new int[] {1,7,4,5,3,2,9,6,8};
  int[] P = b.Select( v => int.Parse(v) ).ToArray();
  
  int min = 99;
  
  ////////////////////////////
  foreach( var q in P ) {
    if ( L[q] < min ) {
      min = L[q];
    }
  }  
  
  ////////////////////////////
  var result = new List<int>();
  while( 0 < N ) {
    foreach( var q in p ) {
      
      if ( !P.Contains(q) ) {        
        continue;
      }
      
      var l = L[q];
      
      bool test = true;
      int n = N - l;
      if ( n != 0 && n < 20 ) {
        int[] C = new int[P.Count()]; 
        test = check( n , L , p , P , C);
      }

      if ( test ) {
        N = n;
        result.Add(q);
        break;
      }
      
    }
  }
  
  ////////////////////////////
  result.Sort( (e,r) => r - e );
  foreach( var q in result ) {
    Console.Write(q);
  }
  
  
}
       
static bool check( int n , int[] L, int[] p, int[] P ,int[] C) {
  int v = 0;
  for(int I=0;I<C.Count();++I) {v += L[P[I]] * C[I];}
  if ( v == n ) {return true;}
  if ( n < v )  {return false;}
	
  var result = false;
  for(int I=0;I<C.Count();++I) {
    var c = new int[C.Count()];
    Array.Copy(C,c,C.Count());
    c[I] += 1;
    result |= check( n,L,p,P, c );
  }
  return result;  
}       
       
}