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 functools import lru_cache
def sub():
    N, M = [int(e) for e in input().split()]
    As = [e for e in input().split()]

    d_cost = {
            "1": 2,
            "2": 5,
            "3": 5,
            "4": 4,
            "5": 5,
            "6": 6,
            "7": 3,
            "8": 7,
            "9": 6,
            }
    
    
    NINF = -10**9
    @lru_cache(maxsize=None)   
    def dp(a_life):
        if a_life == 0:
            return 0
        cc = [a_life - d_cost[a] for a in As]
        cc = [c for c in cc if c >= 0]
        if len(cc) == 0:
            return NINF
        buf = [dp(c) + 1 for c in cc]
        return max(buf)
    
    Lmax = dp(N)
    
    life = N
    buf = []
    for i in range(Lmax):
        oks = [a for a in As if dp(life - d_cost[a]) == dp(life) - 1 and life - d_cost[a] >= 0]
        a_selected = max(oks)
        buf.append(a_selected)
        life = life - d_cost[a_selected]
    print("".join(buf))


sub()