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: Accepted)

# D - Match Matching

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

n_match = [-1,2,5,5,4,5,6,3,7,6]

dp = [-1] * (N+1) # dp[i]はちょうどi本のマッチ棒で作れる最も桁数の多い整数の桁数

dp[0] = 0
for idx in range(1,N+1):
    tmp = []
    for x in A:
        if idx - n_match[x] >= 0:
            tmp.append(dp[idx - n_match[x]] + 1)
    if tmp:
        dp[idx] = max(tmp)

ans = ""
rest_match = N
while len(ans) <= N//2 and rest_match > 0:
    for x in A:
        if rest_match - n_match[x] >= 0 and dp[rest_match - n_match[x]] == dp[rest_match] - 1:
            ans += str(x)
            rest_match -= n_match[x]
            break
            
print(ans)