Appease Inti
The Maya tribe has vanished, the Yule tribe was forced to disband and leave their lands, and now the Auguya tribe faces a similar threat. They have appeased the rain god Tlaloc but neglected the sun god Inti. Feeling overlooked, Inti threatens to unleash a scorching heat unless the tribe presents him with a new collection of charming patterns made from large granite slabs painted in black and white. A charming pattern is defined as a rectangle with a width of W and a height of H, where no 2 by 2 square is entirely one color.
Your task is to determine the K-th lexicographically smallest charming pattern. A pattern is considered lexicographically smaller than another if, when viewed column by column from top to bottom, there is a position where all previously considered slabs match in color, and the slab at this position in the first pattern is white, while in the second it is black.
Input
The input consists of three numbers: W, H, and K (1 ≤ W ≤ 1000, 1 ≤ H ≤ 10, 1 ≤ K ≤ 10^18).
Output
Output the desired charming pattern, using 'w' for white slabs and 'b' for black slabs. If there is no pattern corresponding to the given number, output "Impossible" (without quotes).