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 Python (3.4.3) (judge verdict: Runtime Error)


n, m = map(int, input().split(' '))
ai = list(sorted(map(int, input().split(' '))))
required_maches = {1: 2, 2: 5, 3: 5, 4: 4, 5: 5, 6: 6, 7: 3, 8: 7, 9: 6}

used_numbers = dict()

def evaluate(l):
    if l == None:
        return -9999999999999999999999999999999
    if l == []:
        return 0
    return int(''.join(reversed([str(i) for i in sorted(l)])))

min_maches = min([required_maches[x] for x in ai])
def find(matches_count_to_use):
    if matches_count_to_use not in used_numbers:
        if matches_count_to_use == 0:
            used_numbers[matches_count_to_use] = []
        elif matches_count_to_use < min_maches:
            used_numbers[matches_count_to_use] = None
        else:
            number_to_use = max(ai,
                key=lambda x: evaluate(find(matches_count_to_use - required_maches[x])))
            prev = find(matches_count_to_use - required_maches[number_to_use])
            if prev == None:
                used_numbers[matches_count_to_use] = None
            else:
                used_numbers[matches_count_to_use] = prev + [number_to_use]
    return used_numbers[matches_count_to_use]
    
print(evaluate(find(n)))