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 defaultdict

n, m = map(int, input().split())
A = list(map(int, input().split()))
dic = {1: 2, 2: 5, 3: 5, 4: 4, 5: 5, 6: 6, 7: 3, 8: 7, 9: 6}
usable = defaultdict(int)

for num in A:
    use = dic[num]
    if usable[use] < num:
        usable[use] = num

DP = [-1]*(n+1)
DP[0] = 0

for i in range(n):
    digits = DP[i]
    if digits < 0:
        continue

    for use in usable.keys():
        if i+use <= n and DP[i+use] < digits + 1:
            DP[i+use] = digits + 1
        else:
            continue

digits = DP[n]
num_of_match = n
ans = ''

for _ in range(n):
    if digits == 0:
        break

    for num in sorted(usable.values(), reverse=True):
        use = dic[num]
        if DP[num_of_match - use] == digits - 1:
            digits -= 1
            num_of_match -= use
            ans += str(num)
            break
        else:
            continue

print(ans)