D - Match Matching

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.

20 4
3 7 8 4

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.

101 9
9 8 7 6 5 4 3 2 1

71111111111111111111111111111111111111111111111111

The output may not fit into a $64$-bit integer type.

15 3
5 4 6

654