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)

from collections import Counter


def parse_line(line, type=int):
    return [type(x) for x in line.split(' ')]


#              1, 2, 3, 4, 5, 6, 7, 8, 9
weight = ['x', 2, 5, 5, 4, 5, 6, 3, 7, 6]


def run(k, weight_to_num, cache):
    if k not in cache:
        if k <= 1:
            res = 0
        else:
            res = 0
            for w, num in weight_to_num.items():
                res = max(res, run(k - w, weight_to_num, cache))
            if res > 0:
                res += 1
            if k in weight_to_num:
                res = max(1, res)
        cache[k] = res
    return cache[k]


def main():
    n, m = parse_line(input())
    numbers = set(parse_line(input()))
    if 6 in numbers and 9 in numbers:
        numbers.remove(6)
    if 2 in numbers and 3 in numbers:
        numbers.remove(2)
    if 2 in numbers and 5 in numbers:
        numbers.remove(2)
    if 3 in numbers and 5 in numbers:
        numbers.remove(3)

    weight_to_num = {weight[v]: v for v in numbers}
    cache = {}
    run(n, weight_to_num, cache)
    #print(cache)
    #return

    ws = list(weight_to_num.keys())
    ws.sort(reverse=True, key=lambda w: weight_to_num[w])
    res = []
    cache = {k:v for k,v in cache.items() if v > 0}
    cache[0] = 0

    l = cache[n]
    while l:
        for w in ws:
            if cache.get(n - w, 'False') == l - 1:
                res.append(weight_to_num[w])
                n = n - w
                l -= 1
                break
    print(''.join((str(x) for x in res)))


if __name__ == '__main__':
    main()

# 20 4
# 3 7 8 4