The Way Home

Returning home after an exciting game at Vinni Puh's place, the donkey Ia decided to take a walk. While walking, he kept thinking about his approaching birthday and didn't notice when he got lost.

It is known that during his walk, Ia always moves according to a certain algorithm. At first, he always starts by moving northeast, taking one step (thus arriving at the point $(1,1)$). Then, he changes direction to southeast, then southwest, then northwest, and so on. Each time Ia changes direction, he takes $N$ more steps than he did during the previous change of direction.

When Ia decided to return home, he found himself deep in the forest. Dusk was approaching, and Ia wanted to get home as quickly as possible.

It is known that sunset will occur in $T$ hours, and the donkey's speed is $V$ steps per hour (each step is of constant length). Ia starts from $(0,0)$, and his house is located at (hx, hy). Ia changed direction $K$ times.