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 PyPy3 (2.4.0) (judge verdict: Accepted)

def strmax(a, b):
    if len(a) > len(b):
        return a
    elif len(a) < len(b):
        return b
    else:
        return max(a, b)


def main():
    N, M = map(int, input().split())
    A = list(map(int, input().split()))
    dp = [None] * (N+1)
    dp[0] = ""
    cost = [0, 2, 5, 5, 4, 5, 6, 3, 7, 6]
    for i in range(N+1):
        for d in A:
            if i < cost[d]:
                continue
            prev = dp[i - cost[d]]
            if prev is None:
                continue
            else:
                candidate = strmax(prev + str(d),
                                   str(d) + prev)
            if dp[i] is None:
                dp[i] = candidate
            else:
                dp[i] = strmax(dp[i], candidate)
    print(dp[N])


if __name__ == "__main__":
    main()