# PROBLEM LINK:

**Setter:** Mladen Puzic

**Tester:** Michael Nematollahi

**Editorialist:** Taranpreet Singh

# DIFFICULTY:

# PREREQUISITES:

Basic Math.

# PROBLEM:

You are given the number of points scored by Chef and Paja being X and Y in a game of Ping Pong. You are also given integer K. For first K games, Chef serves, for next K games, Paja serves, then for next K games, Chef serves and so on.

Find out who shall take the next serve.

# EXPLANATION

Since Chef has X points and Paja has Y points, We know a total of X+Y games have been played till now. Thatâ€™s all we need to find out who serves in next game.

Letâ€™s number games played till now from 0 to X+Y-1, so we want to find who serves in game numbered X+Y. Let us write Z = X+Y as

We can see that for every 2*K games, Chef serves in first K games, Paja serves in next K games. So, We can easily state that the person serving in game i shall be the person serving in game (i-2*K*c) where c \geq 0 and (i-2*K*c) \geq 0 holds. Hence, we can easily reduce that person serving in game X+Y is same as person serving in game Z = (X+Y) \% (2*K).

Now, we have 0 \leq Z < 2*K and we want to know who serves in game Z. We know, Chef serves in games in range [0, K-1] and Paja serves in games in range [K, 2*K-1] out of first 2*K games, we can easily check whether Z lies in [0, K-1] or [K, 2*K-1] and print answer accordingly.

**Bonus Problem:**

Find out the number games in which Chef has served, if Chef scored X points and Paja scored Y points.

# TIME COMPLEXITY

Time complexity is O(1) per test case.

# SOLUTIONS:

## Setter's Solution

```
#include<bits/stdc++.h>
using namespace std;
int main() {
ios::sync_with_stdio(false); cin.tie(0); cout.tie(0); cerr.tie(0);
int T; cin >> T;
while(T--) {
int X, Y, K;
cin >> X >> Y >> K;
long long totalPoints = X+Y; ///we are only interested in the total number of points
long long pointRemainder = totalPoints%(2*K); ///how many points since Chef last started serving
if(pointRemainder < K) { ///if in current round, Chef hasn't served K times, then he serves
cout << "Chef\n";
} else { ///otherwise, Paja serves
cout << "Paja\n";
}
}
return 0;
}
```

## Tester's Solution

```
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
#define F first
#define S second
int main(){
ios::sync_with_stdio(false);
cin.tie(0);
int te; cin >> te;
while (te--){
int x, y, k; cin >> x >> y >> k;
int sm = x+y;
sm /= k;
if (sm&1)
cout << "Paja\n";
else
cout << "Chef\n";
}
return 0;
}
```

## Editorialist's Solution

```
import java.util.*;
import java.io.*;
import java.text.*;
class PAJAPONG{
//SOLUTION BEGIN
void pre() throws Exception{}
void solve(int TC) throws Exception{
long x = nl(), y = nl(), k = nl();
long d = x+y;
if((d/k)%2 == 0)pn("Chef");
else pn("Paja");
}
//SOLUTION END
void hold(boolean b)throws Exception{if(!b)throw new Exception("Hold right there, Sparky!");}
DecimalFormat df = new DecimalFormat("0.00000000000");
static boolean multipleTC = true;
FastReader in;PrintWriter out;
void run() throws Exception{
in = new FastReader();
out = new PrintWriter(System.out);
//Solution Credits: Taranpreet Singh
int T = (multipleTC)?ni():1;
pre();for(int t = 1; t<= T; t++)solve(t);
out.flush();
out.close();
}
public static void main(String[] args) throws Exception{
new PAJAPONG().run();
}
int bit(long n){return (n==0)?0:(1+bit(n&(n-1)));}
void p(Object o){out.print(o);}
void pn(Object o){out.println(o);}
void pni(Object o){out.println(o);out.flush();}
String n()throws Exception{return in.next();}
String nln()throws Exception{return in.nextLine();}
int ni()throws Exception{return Integer.parseInt(in.next());}
long nl()throws Exception{return Long.parseLong(in.next());}
double nd()throws Exception{return Double.parseDouble(in.next());}
class FastReader{
BufferedReader br;
StringTokenizer st;
public FastReader(){
br = new BufferedReader(new InputStreamReader(System.in));
}
public FastReader(String s) throws Exception{
br = new BufferedReader(new FileReader(s));
}
String next() throws Exception{
while (st == null || !st.hasMoreElements()){
try{
st = new StringTokenizer(br.readLine());
}catch (IOException e){
throw new Exception(e.toString());
}
}
return st.nextToken();
}
String nextLine() throws Exception{
String str = "";
try{
str = br.readLine();
}catch (IOException e){
throw new Exception(e.toString());
}
return str;
}
}
}
```

Feel free to Share your approach, if you want to. (even if its same ) . Suggestions are welcomed as always had been.