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 Scala (2.11.7) (judge verdict: Accepted)

import scala.io.StdIn.readLine

object Main{
  def main(args : Array[String]): Unit ={
    val Array(n, m) : Array[Int] = readLine().split(' ').map(_.toInt)
    val can : Array[Int] = readLine().split(' ').map(_.toInt)
    val SLV = new SOLVE(n, can)
    println(SLV.solve(n))
  }
}

class SOLVE(private val n : Int, private val can : Array[Int]){
  val COST : Array[Int] = Array(0, 2, 5, 5, 4, 5, 6, 3, 7, 6)
  val DP : Array[BigInt] = Array.fill(n + 10)(-1)
  DP(0) = 0
  def solve(k : Int): BigInt ={
    /*
    if(DP(k) != -1) DP(k)
    else{
      for(ele <- can){
        val idx = k - COST(ele)
        if(idx >= 0) if(DP(k) < ele + 10 * solve(idx)) DP(k) = ele + 10 * solve(idx)
      }
    }
    DP(k)
    */
    for(i <- 0 until k; j <- can){
      val idx : Int = i + COST(j)
      if(DP(idx) < 10 * DP(i) + j) DP(idx) = 10 * DP(i) + j
    }
    DP(k)
  }
}