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: Wrong Answer)

import itertools
from collections import defaultdict

N,M = map(int,input().split())
A = [int(x) for x in input().split()]
L = [100,2,5,5,4,5,6,3,7,6]

l_to_n = [[] for _ in range(10)]
for a in A:
  l_to_n[L[a]].append(a)
  
l_to_n = [(i,max(x)) for i,x in enumerate(l_to_n) if x]

se = {0} # 100以下で作れる長さ

for l,_ in l_to_n:
  se = {x+y for x,y in itertools.product(se,range(0,100,l)) if x+y < 100}

answer = ''
m_L,x = l_to_n[0]
while N > 100:
  N -= m_L
  answer += str(x)
  
for l,x in l_to_n:
  while N-l in se:
    N -= l
    answer += str(x)
  if N == 0:
    break

answer = ''.join(sorted(answer,reverse=True))

print(answer)