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: Time Limit Exceeded)

# match matching
N, M = map(int, input().split())
ok = list(map(int, input().split()))
ok.sort()
a = [i for i in range(1, 10)]
b = [2, 5, 5, 4, 5, 6, 3, 7, 6]

data = {a[i]: b[i] for i in range(9)}

dp = [[0 for i in range(N+1)] for j in range(M+1)]

for i in range(M):
    for cnt in range(N+1):
        for j in range(M):
            num = ok[j]
            cost = data[num]
            if cnt > cost:
                P = len(str(dp[i+1][cnt-cost]))
                if dp[i + 1][cnt-cost] > 0:
                    dp[i+1][cnt] = max(dp[i+1][cnt-cost] +
                                       num*10 ** P, dp[i+1][cnt])
                else:
                    dp[i+1][cnt] = max(dp[i+1][cnt-cost], dp[i+1][cnt])
            elif cnt == cost:
                dp[i+1][cnt] = max(num, dp[i+1][cnt])
            elif cnt < cost:
                dp[i+1][cnt] = max(dp[i][cnt], dp[i+1][cnt])

ans = dp[M][N]
print(ans)