Black Square#2371
Inspired by Kazimir Malevich's masterpiece "Black Square," Peter Palevich decided to create his own version. He prepared a rectangular grid of m \times n white cells, arranged in rows of cells each.
Peter painted some of the cells black, so that the black cells formed a square of size s \times s. However, the next day, Peter became disappointed with his creation and destroyed it by cutting the canvas into horizontal stripes of size 1 \times n and burning them in the fireplace.
The following morning, Peter changed his mind and decided to restore the painting. He searched the fireplace for remains and, fortunately, one of the stripes, namely the -th from the top, survived the fire.
Now Peter wonders if it is possible to restore the painting based on this stripe. Help him to do so.
The first line contains four integers: , , , and (1 \leq m, n \leq 5000, 1 \leq s \leq \min(m, n), 1 \leq k \leq m).
The second line contains characters, describing the -th row of the painting: . denotes a white cell, and * denotes a black cell.
If the initial painting can be uniquely restored, output Unique. If there are several possible variants, output Ambiguous. If no such painting is possible, output Impossible.
Example 1
Example 2
Example 3