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: Wrong Answer)

import java.util.*

fun main(args: Array<String>) {
    val count = arrayOf(-1, 2, 5, 5, 4, 5, 6, 3, 7, 6)

    val sc = Scanner(System.`in`)
    val n = sc.nextInt()
    val m = sc.nextInt()
    val a = IntArray(m) { sc.nextInt() }.sorted()
    val numbers = a.fold(mutableMapOf<Int, Int>()) { acc, i ->
        val need = count[i]
        if (!acc.containsKey(need)) {
            acc[need] = i
        } else if (acc[need]!! < i) {
            acc[need] = i
        }

        acc
    }

    val numbersCount = numbers.map { it.value }.map { count[it] }.sorted()
    val minCount = numbersCount.first()

    val lcm = numbersCount.fold(1, ::lcm)
    val maxNum = Array<Pair<Int, List<Int>>>(lcm + 1) {
        when (it) {
            0 -> 0 to emptyList()
            else -> -1 to emptyList()
        }
    }

    maxNum.forEachIndexed { index, p ->
        if (p.first < 0) return@forEachIndexed

        numbers.forEach { entry ->
            val (need, num) = entry
            if (index + need < maxNum.size && maxNum[index + need].first < p.first + 1) {
                maxNum[index + need] = p.first + 1 to (p.second + num)
            }
        }

    }

    val r = (0..maxNum.size)
        .first { (n - it) % numbersCount.first() == 0 && maxNum[it].first >= 0 }

    val ret = (IntArray((n - r) / minCount) { numbers[minCount]!! }.toList() + maxNum[r].second)
        .sorted().reversed().joinToString(separator = "")
    println(ret)
}

fun gcd(a: Int, b: Int): Int {
    val c = a % b
    return if (c == 0) b else gcd(b, c)
}

fun lcm(a: Int, b: Int): Int {
    return a * b / gcd(a, b)
}