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 java.io._
import java.util.StringTokenizer
import scala.util.control.Breaks.{breakable,break}
import scala.collection.mutable.{Map, Queue, PriorityQueue}

object Main extends App {
  val in = new InputReader(System.in)
  val pw = new PrintWriter(System.out)

  val N, M = in.next().toInt
  val A = new Array[Int](M)
  for (i <- 0 until M)
    A(i) = in.next().toInt

  //
  val map = Map(
    1 -> 2, 2 -> 5, 3 -> 5,
    4 -> 4, 5 -> 5, 6 -> 6,
    7 -> 3, 8 -> 7, 9 -> 6
  )


  val dp = new Array[Int](N+1)
  val init = -1
  for (i <- 0 to N)
    dp(i) = init

  dp(0) = 0
  for (i <- 1 to N) {
    for (e <- A) {
      val diff = i - map(e)
      if (diff >= 0) {
        if (dp(i) == 0)
          dp(i) = dp(diff) + 1
        else
          dp(i) = Math.max(dp(i), dp(diff) + 1)
      }
    }
  }

  var now = N
  var ans = ""
  while (now > 0) {
    breakable {
      for (i <- (1 to 9).reverse) {
        val diff = now - map(i)
        if (A.contains(i) && diff >= 0) {
          if (dp(diff) == dp(now) - 1) {
            now = diff
            ans += i.toString
            break
          }
        }
      }
    }
  }

  println(ans)
}


class InputReader(stream: InputStream) {
  private val reader = new BufferedReader(new InputStreamReader(stream))
  private var tokenizer: StringTokenizer = new StringTokenizer(reader.readLine())
  def next(): String = {
    while (!tokenizer.hasMoreTokens()) {
      tokenizer = new StringTokenizer(reader.readLine())
    }
    tokenizer.nextToken()
  }
}