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)

import copy

N, M = list(map(int, input().split()))
A = list(map(int, input().split()))

t = [0, 2, 5, 5, 4, 5, 6, 3, 7, 6]
L = {}
for i in A:
  if t[i] in L:
    if L[t[i]] < i:
      L[t[i]] = i
  else:
    L[t[i]] = i
  
dp = [[0 for j in range(10)] for i in range(N)]
for i in L.items():
  dp[i[0] - 1][i[1]] = 1
for i in range(N):
  if max(dp[i]) == 0:
    continue
  for j in L.items():
    k = i + j[0]
    if k < N:
      t = copy.deepcopy(dp[i])
      t[j[1]] += 1
      if sum(t) > sum(dp[k]):
        tt = dp[k]
        dp[k] = t
        del tt
      else:
        for ii in range(9, 0, -1):
          if t[ii] > dp[k][ii]:
            tt = dp[k]
            dp[k] = t
            del tt
            break
          elif t[ii] < dp[k][ii]:
            break
          
t = dp[-1]
Ans = ""
for i in range(9, 0, -1):
  for j in range(t[i]):
    Ans += str(i)
    
print(Ans)