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 Kotlin (1.0.0) (judge verdict: Accepted)

import java.lang.StringBuilder

fun main(args: Array<String>) {
    val (N, M) = readLine()!!.split(" ").map{it.toInt()}
    val A = readLine()!!.split(" ").map{it.toInt()}.sorted()

    val matches = arrayOf(100, 2, 5, 5, 4, 5, 6, 3, 7, 6)
    val dp = Array(M + 1) { Array(N + 1) {-1}  }
    val prev = Array(M + 1) { Array(N + 1) {Pair(-1, -1)}  }

    dp[0][0] = 0

    for (i in A.indices) {
        for (k in dp[i].indices) {
            dp[i + 1][k] = dp[i][k]
            prev[i + 1][k] = Pair(i, k)

            if (k >= matches[A[i]] && dp[i + 1][k] <= dp[i + 1][k - matches[A[i]]] + 1) {
                dp[i + 1][k] = dp[i + 1][k - matches[A[i]]] + 1
                prev[i + 1][k] = Pair(i + 1, k - matches[A[i]])
            }
        }
    }

    val res = StringBuilder()
    var p = Pair(A.size, N)

    while (p.first > 0) {
        val q = prev[p.first][p.second]
        if (p.first == q.first) {
            res.append(A[p.first - 1])
        }
        p = q
    }

    println(res.toString())
}