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 Go (1.6) (judge verdict: Wrong Answer)

package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
	"strings"
)

func getNextLine(scanner *bufio.Reader) string {
	var buffer string
	for {
		line, isPrefix, _ := scanner.ReadLine()
		buffer += string(line)
		if isPrefix == false {
			break
		}
	}
	return buffer
}

func getIntList(scanner *bufio.Reader) []int {
	list := strings.Split(getNextLine(scanner), " ")
	l := len(list)
	result := make([]int, l)
	for i := 0; i < l; i++ {
		result[i], _ = strconv.Atoi(list[i])
	}
	return result
}

func main() {
	fp := os.Stdin
	if len(os.Args) > 1 {
		fp, _ = os.Open(os.Args[1])
	}

	scanner := bufio.NewReader(fp)

	var n, m int
	usage := []int{0, 2, 5, 5, 4, 5, 6, 3, 7, 6}
	sorted := []int{1, 7, 4, 5, 3, 2, 9, 6, 8}
	fmt.Sscan(getNextLine(scanner), &n, &m)

	aaa := getIntList(scanner)
	exists := make([]int, 0)
	counts := make([]int, m)
	for i := 0; i < 9; i++ {
		for j := 0; j < m; j++ {
			if sorted[i] == aaa[j] {
				exists = append(exists, aaa[j])
				break
			}
		}
	}

	dfs(n, m, exists, counts, usage)
	for i := 9; i > 0; i-- {
		for j := 0; j < m; j++ {
			if i != exists[j] {
				continue
			}
			for k := 0; k < counts[j]; k++ {
				fmt.Print(i)
			}
		}
	}
	fmt.Println("")
}

func dfs(n int, m int, exists []int, counts []int, usage []int) bool {
	sum := n
	for i := 0; i < m; i++ {
		sum -= counts[i] * usage[exists[i]]
	}
	if sum == 0 {
		return true
	}
	if sum < 0 {
		return false
	}
	for i := 0; i < m; i++ {
		counts[i]++
		found := dfs(n, m, exists, counts, usage)
		if found == true {
			return true
		}
		counts[i]--
	}
	return false
}