Help in ping paja pong

Guys, I have checked this question solutions everyone is doing same ((x+y)/k)%2==0
checking this condition but i am to able to understand why, please tell me
link of question is https://www.codechef.com/problems/PAJAPONG

Which part don’t you understand? X + Y is the total sum of moves, \left \lfloor \dfrac{X + Y}{K} \right \rfloor is the number of times the server has changed, so \left \lfloor \dfrac{X + Y}{K} \right \rfloor \mod 2 will be 1 iff the server is Paja.

Hope this help!

for _ in range(int(input())):
    	x,y,k=map(int, input().split())
    	#fin total score 
    	total_score=x+y
    	#find how many services are done yet
    	service_changed_yet=total_score//k
    	#if service yet are even then next service of chef else paja
    	if(service_changed_yet%2==0):
    		print("Chef")
    	else:
    		print("Paja")