# BELLA CIAO (CHFHIEST) Solution — Codechef JuneLong Challenge

**Problem Statement**

Chef is planning a heist in the reserve bank of Chefland. They are planning to hijack the bank for D days and print the money. The initial rate of printing the currency is P dollars per day and they increase the production by Q dollars after every interval of d days. For example, after d days the rate is P+Q dollars per day, and after 2d days the rate is P+2Q dollars per day, and so on. Output the amount of money they will be able to print in the given period.

# Input

- The first line contains an integer T, the number of test cases. Then the test cases follow.
- Each test case contains a single line of input, four integers D,d,P,Q.

# Output

For each test case, output in a single line the answer to the problem.

# Constraints

- 1≤T≤10⁵
- 1≤d≤D≤10⁶
- 1≤P,Q≤10⁶

# Subtasks

**Subtask #1 (15 points):** d≤D≤100

**Subtask #2 (85 points):** original constraints

# Sample Input

`3`

2 1 1 1

3 2 1 1

5 2 1 2

# Sample Output

`3`

4

13

# Explanation

**Test Case **1**:**

- On the first day, the rate of production is 1 dollar per day so 1 dollar is printed on the first day.
- On the second day, the rate of production is 1+1=2 dollars per day so 2 dollars are printed on the second day.
- The total amount of money printed in 2 days is 1+2=3 dollars.

**Test Case **2**:**

- For the first two days, the rate of production is 1 dollar per day so 1⋅2=2 dollars are printed on the first two days.
- On the third day, the rate of production is 1+1=2 dollars per day so 2 dollars are printed on the third day.
- The total amount of money printed in 3 days is 2+2=4 dollars.

**Test Case **3**:**

- For the first two days, the rate of production is 1 dollar per day so 1⋅2=2 dollars are printed on the first two days.
- On the next two days, the rate of production is 1+2=3 dollars per day so 3⋅2=6 dollars are printed on the next two days.
- On the last day, the rate of production is 3+2=5 dollars per day so 5 dollars are printed on the last day.
- The total amount of money printed in 5 days is 2+6+5=13 dollars.

**Code (Solution)**

The code has been implemented in Java

`import java.util.*;`

import java.lang.*;

import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */

class Codechef

{

public static void main (String[] args) throws java.lang.Exception

{

//SOLUTION

FastReader sc = new FastReader();

long t = sc.nextLong();

while(t-- > 0){

long D,d,p,q;

D = sc.nextLong();

d = sc.nextLong();

p = sc.nextLong();

q = sc.nextLong();

long n = D/d;

long sol=0;

sol= n*p*d + q*d*(n*(n-1))/2 + (D%d)*(p+n*q);

System.out.println(sol);

}

}

// Below are just the classes needed for fast Input in Java with Fast Reader

static class FastReader {

BufferedReader br;

StringTokenizer st;

public FastReader() {

br = new BufferedReader(new InputStreamReader(System.in));

}

String next() {

while (st == null || !st.hasMoreElements()) {

try {

st = new StringTokenizer(br.readLine());

} catch (IOException e) {

e.printStackTrace();

}

}

return st.nextToken();

}

int nextInt() {

return Integer.parseInt(next());

}

long nextLong() {

return Long.parseLong(next());

}

double nextDouble() {

return Double.parseDouble(next());

}

String nextLine() {

String str = "";

try {

str = br.readLine();

} catch (IOException e) {

e.printStackTrace();

}

return str;

}

}

}

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**References**

(Video Editorial Link For Better Explanation)