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)

from bisect import bisect_left
N, M = map(int, input().split())
nums = list(map(int, input().split()))

matchNum = {
    1 : 2,
    2 : 5,
    3 : 5,
    4 : 4,
    5 : 5,
    6 : 6,
    7 : 3,
    8 : 7,
    9 : 6,
}

dp = [''] * (N + 1)
for n in range(1, N + 1):
    for k in nums:
        d = 0
        cnt = n - matchNum[k]
        if cnt < 0 or cnt >= 1 and dp[cnt] == '':
            continue
        if cnt == 0 or dp[n] == '' or dp[n] <= dp[cnt] * 10:
            oldVal = list(str(dp[cnt]))[:: -1]
            adder = bisect_left(oldVal, str(k))
            newVal = oldVal[:adder] + [str(k)] + oldVal[adder:]
            newVal = int(''.join(newVal[:: -1]))
            d = max(d, newVal)
        if d == 0:
            continue
        elif dp[n] == '':
            dp[n] = d
        else:
            dp[n] = max(dp[n], d)

print(dp[N])