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: Accepted)

package main

import (
	"fmt"
	"io"
	"os"
	"sort"
)

func fscanNums(r io.Reader, len int) (nums []int) {
	var num int
	for i := 0; i < len; i++ {
		fmt.Fscan(r, &num)
		nums = append(nums, num)
	}
	return
}

func max(a, b int) int {
	if a > b {
		return a
	}
	return b
}

func answer(r io.Reader, w io.Writer) {

	msSizes := []int{0, 2, 5, 5, 4, 5, 6, 3, 7, 6}

	var numMS int
	var numDigits int
	fmt.Fscan(r, &numMS)
	fmt.Fscan(r, &numDigits)
	nums := fscanNums(r, numDigits)
	sort.Sort(sort.Reverse(sort.IntSlice(nums)))

	dp := make([]int, numMS+1)
	dp[0] = 0
	for i := 1; i <= numMS; i++ {
		maxDigit := -1
		for j := 0; j < numDigits; j++ {
			index := i - msSizes[nums[j]]
			if index >= 0 && dp[index] >= 0 {
				maxDigit = max(maxDigit, dp[index]+1)
			}
		}
		dp[i] = maxDigit
	}

	remain := numMS
	for remain > 0 {
		maxDigit := -1
		for j := 0; j < numDigits; j++ {
			index := remain - msSizes[nums[j]]

			if index >= 0 && dp[index] == dp[remain]-1 {
				maxDigit = max(maxDigit, nums[j])
			}
		}
		remain = remain - msSizes[maxDigit]
		fmt.Fprintf(w, "%v", maxDigit)
	}
}

func main() {
	answer(os.Stdin, os.Stdout)
}