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 PHP7 (7.0.15) (judge verdict: Accepted)

<?php

fscanf(STDIN, "%d %d", $n, $m);
$A = array_map('intval', explode(' ', trim(fgets(STDIN))));

$M = [2, 5, 5, 4, 5, 6, 3, 7, 6, ];
$RM = [
    2 => [1],
    3 => [7],
    4 => [4],
    5 => [2, 3, 5],
    6 => [6, 9],
    7 => [8],
];

// プラスするマッチの本数の配列
$AM = [];
foreach ($A as $v) {
    $AM[] = $M[$v - 1];
}
sort($AM);
$AM = array_unique($AM);
// マッチの本数から数字を逆算する配列
$ARM = [];
foreach ($AM as $v) {
        $ARM[$v] = max(array_intersect($RM[$v], $A));
}

const N_MAX = 10005;
$dp = array_fill(0, N_MAX, '');
// 初期化
foreach ($AM as $v) {
    $dp[$v] = $ARM[$v];
}
for ($i = 0; $i < N_MAX; ++$i) {
    foreach ($AM as $v) {
        if ($i - $v >= 0 && $dp[$i - $v] !== '') {
            chmax($dp[$i], $dp[$i - $v], $ARM[$v]);
        }
    }
}

function chmax(&$a, $b, $c) {
    if (strlen($a) > strlen($b) + 1) {
        // 何もしない
    } else if (strlen($a) === strlen($b) + 1) {
        // 比較して大きい方にする
        if ($a < ($b . $c)) $a = $b . $c;
    } else {
        // b + $cで置き換え
        $a = $b . $c;
    }
}

/* echo implode(', ', $dp), PHP_EOL; */

echo $dp[$n];