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)

from collections import defaultdict

def f(a, b):
    for i in range(9,0,-1):
        if a[i] == b[i]: continue
        elif a[i] > b[i]:
            return True
        else:
            return False
    return False

N, M = map(int, input().split())
se = set()
A = list(map(int, input().split()))
toNum = [0, 2, 5, 5, 4, 5, 6, 3, 7, 6]
dp = [[] for i in range(N+1)]
done = [False for i in range(N+10)]
done[N] = True
dics = [defaultdict(int) for i in range(N+1)]
for i in range(N-1, -1, -1):
    for a in A:
        num = toNum[a]
        if not done[i+num]: continue
        l = len(dp[i+num])+1
        d = dics[i+num].copy()
        d[a] += 1
        if l > len(dp[i]) or (l == len(dp[i]) and f(d, dics[i])):
            dp[i] = dp[i+num] + [a]
            done[i] = True
            dics[i] = d
dp[0].sort(reverse=True)
print(*dp[0], sep='')