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 Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.util.*;

class Main {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        String[] nm = scanner.nextLine().split(" ", 2);
        int n = Integer.parseInt(nm[0]);
        int m = Integer.parseInt(nm[1]);

        int[] dispatch = { 0, 2, 5, 5, 4, 5, 6, 3, 7, 6 };

        String[] line = scanner.nextLine().split(" ", m);
        int[] nums = new int[m];
        for (int i = 0; i < m; i++) {
            nums[i] = Integer.parseInt(line[i]);
        }

        int[][] dp = new int[n+1][1];
        int[] dpSize = new int[n+1];
        dynamicProgramming(dp, dpSize, 0, n, m, nums, dispatch);
        for (int i = 0; i < dpSize[n]; i++) {
            System.out.print(dp[n][i]);
        }
        System.out.print("\n");
    }

    private static void dynamicProgramming(int[][] dp, int[] dpSize, int i, int n, int m, int[] nums, int[] dispatch) {
        int remaining = n - i;
        for (int j = 0; j < m; j++) {
            int num = nums[j];
            int willUse = dispatch[num];
            if (willUse > remaining) continue;
            if (i + willUse > n) continue;

            /* next num */
            int nextSize = dpSize[i] + 1;
            int[] next = new int[nextSize];
            boolean numUsed = false;
            int nextInd = 0;
            for (int dpInd = 0; dpInd < dpSize[i]; dpInd++) {
                if (numUsed) {
                    next[nextInd] = dp[i][dpInd];
                    nextInd++;
                } else {
                    if (num > dp[i][dpInd]) {
                        next[nextInd] = num;
                        nextInd++;
                        next[nextInd] = dp[i][dpInd];
                        nextInd++;
                        numUsed = true;
                    } else {
                        next[nextInd] = dp[i][dpInd];
                        nextInd++;
                    }
                }
            }
            if (!numUsed) {
                next[nextInd] = num;
            }

            if (compare(dp[i + willUse], dpSize[i + willUse], next, nextSize) < 0) {
                dp[i + willUse] = next;
                dpSize[i + willUse] = nextSize;
                dynamicProgramming(dp, dpSize, i + willUse, n, m, nums, dispatch);
            }
        }
    }

    private static int compare(int[] a, int aSize, int[] b, int bSize) {
        if (aSize != bSize) {
            return aSize - bSize;
        } else {
            for (int i = 0; i < aSize; i++) {
                if (a[i] != b[i]) {
                    return a[i] - b[i];
                }
            }
            return 0;
        }
    }
}