Python Code

By replacing the $1$st digit of $*3,$ it turns out that six of the nine possible values: $13,23,43,53,73,$ and $83,$ are all prime.

By replacing the $3$rd and $4$th digits of $56**3$ with the same digit, this $5-$digit number is the first example having seven primes among the ten generated numbers, yielding the family: $56003,56113,56333,56443,56663,56773,$ and $56993.$ Consequently $56003,$ being the first member of this family, is the smallest prime with this property.

Find the smallest N$-$digit prime which, by replacing K$-$digits of the number $($not necessarily adjacent digits$)$ with the same digit, is part of an L prime value family.

Note$1$: It is guaranteed that solution does exist.

Note$2$: Leading zeros should not be considered.

Note$3$: If there are several solutions, choose the "lexicographically" smallest one $($one sequence is considered "lexicographically" smaller than another if its first element which does not match the corresponding element in another sequence is smaller$)$

Input Format

Input contains three integers N$,$ K and L$.$

Output Format

Print the first L numbers of the prime value family found in increasing order.

Constraints

$2<=$N$<=7$

$1<=$K$<=$N

$1<=$L$<=8$

Sample Input#$00$

$527$

Sample Output#$00$

$56003561135633356443566635677356993$

Sample Input#$01$

$213$

Sample Output#$01$

$111317$