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)

import sys
sys.setrecursionlimit(10**9)
INF=10**18
MOD=10**9+7
def input():
    return sys.stdin.readline().rstrip()

def main():
    N,M=map(int,input().split())
    A=list(map(int,input().split()))
    A.sort()
    for a in A:
        if a==3:
            try:
                A.remove(2)
            except:
                pass
        elif a==5:
            try:
                A.remove(2)
            except:
                pass
            try:
                A.remove(3)
            except:
                pass
        elif a==9:
            try:
                A.remove(6)
            except:
                pass
    d={1:2,2:5,3:5,4:4,5:5,6:6,7:3,8:7,9:6}
    l=[d[x] for x in A]
    dp=[[0]*(N+1) for _ in range(len(l)+1)]
    prev_w=[[0]*(N+1) for _ in range(len(l)+1)]
    real_w=[[0]*(N+1) for _ in range(len(l)+1)]
    for num in range(len(l)):
        for w in range(N+1):
            if w>=l[num]:
                if dp[num+1][w]<dp[num+1][w-l[num]]+1 and real_w[num+1][w-l[num]]+l[num]==w:
                    dp[num+1][w]=dp[num+1][w-l[num]]+1
                    prev_w[num+1][w]=w-l[num]
                    real_w[num+1][w]=w
            if dp[num+1][w]<dp[num][w]:
                dp[num+1][w]=dp[num][w]
                prev_w[num+1][w]=w
                real_w[num+1][w]=w
    l2=[]
    cur_w=N
    for num in range(len(l)-1,-1,-1):
        while True:
            if prev_w[num+1][cur_w]==cur_w-l[num]:
                l2.append(str(A[num]))
                cur_w=prev_w[num+1][cur_w]
            else:
                cur_w=prev_w[num+1][cur_w]
                break
    print(''.join(l2))

if __name__ == '__main__':
    main()