Vampire Numbers
Ilya has a keen interest in mathematics, particularly in a concept known as vampire numbers. These numbers have captivated him so much that he frequently creates and solves problems involving them.
A number a, with a decimal representation of n digits (where n is even), is defined as a vampire number if it can be expressed as the product of two n/2-digit numbers b and c. Additionally, the digits of b and c can be rearranged to form the number a. Each digit must be used exactly as many times as it appears in the combined digits of b and c. The numbers b and c are referred to as the fangs of the number a.
For instance, the number 6880 qualifies as a vampire number because 6880=80×86, whereas the number 1023 does not.
Ilya's latest challenge for you is to identify k distinct vampire numbers, each with n digits.
Input
The input consists of a single line containing two integers k and n — the number of vampire numbers needed and the number of digits in each, respectively (1 ≤ k ≤ 100, 4 ≤ n ≤ 100, with n being even).
Output
Output k distinct n-digit vampire numbers in the format A_i=B_ixC_i, where A_i is the i-th vampire number found, and B_i and C_i are its fangs. The lowercase letter "x" should be placed between B_i and C_i.
If multiple solutions exist, any valid set can be printed. It is guaranteed that for the given n and k, there are k distinct n-digit vampire numbers available.