No.775 tatyam and Prime Daifugo (hard)
tatyam
Shuz*Notice
This problem is a truly terrible problem, so if possible we would like you to enjoy the other problems first, and therefore, once you have solved the other problems and have free time, and moreover that free time
Problem Statement
tatyam is playing Prime Daifugo with extended rules.
In this version of Prime Daifugo, cards with numbers from 1 to 99 written on them are used, and you can play the numbers in your hand by concatenating them if the result is a prime.
tatyam has started wanting to look for the largest prime obtainable by rearranging.
Among the numbers tatyam can make using all the cards in the hand, output $K$ of them in descending order, starting from the largest.
Input
$N\ K$ $a_1$ $a_2$ $\cdots$ $a_N$
$1≤N≤100$
$1≤K≤1000$
$1≤a_i≤99$
There are at least $K$ distinct numbers that can be made by rearranging.
Output
Among the numbers that can be made by rearranging $a_i$, output $K$ of them in descending order, starting from the largest, separated by newlines.
Sample
Sample 1
Input
1 1 2
Output
2
Sample 2
Input
5 5 2 4 6 8 11
Output
864211 864112 862411 862114 861142
Sample 3
Input
5 3 1 7 7 9 13
Output
977131 977113 971713
Sample 4
Input
10 10 99 98 96 94 92 90 88 86 85 82
Output
99989694929088868582 99989694929088868285 99989694929088858682 99989694929088858286 99989694929088828685 99989694929088828586 99989694929086888582 99989694929086888285 99989694929086858882 99989694929086858288
Sample 5
Input
36 3 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 77 77 77 77 77 77 77 77 77 77 77 77 77 77 77 77 77 77 6 5
Output
777777777777777777777777777777777777777777777777777765 777777777777777777777777777777777777777777777777777756 777777777777777777777777777777777777777777777777777675
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