# Chef and Bulb Invention | CodeChef Solution

Hello coders, today we are going to solve Chef and Bulb Invention CodeChef Solution whose Problem Code is CHFINVNT.

Chef is trying to invent the light bulb that can run at room temperature without electricity. So he has N gases numbered from 0 to N âˆ’ 1 that he can use and he doesn’t know which one of the N gases will work but we do know it.

Now Chef has worked on multiple search algorithms to optimize search. For this project, he uses a modulo-based search algorithm that he invented himself. So first he chooses an integer K and selects all indices i in increasing order such that i mod K = 0 and test the gases on such indices, then all indices i in increasing order such that i mod K = 1, and test the gases on such indices, and so on.

Given N, the index of the gas p that will work, and K, find after how much time will he be able to give Chefland a new invention assuming that testing 1 gas takes 1 day.

For example, consider N = 5, p = 2 and K = 3.

• On the 1st day, Chef tests gas numbered 0 because 0 mod 3 = 0.
• On the 2nd day, Chef tests gas numbered 3 because 3 mod 3 = 0.
• On the 3rd day, Chef tests gas numbered 1 because 1 mod 3 = 1.
• On the 4th day, Chef tests gas numbered 4 because 4 mod 3 = 1.
• On the 5th day, Chef tests gas numbered 2 because 2 mod 3 = 2.

So after 5 days, Chef will be able to give Chefland a new invention

## Input Format

• The first line of the input contains a single integer T denoting the number of test cases. The description of T test cases follows.
• The first and only line of each test case contains three space-separated integers N, p, and K.

## Output Format

For each test case, print a single line containing one integer â€” after how much time Chef will be able to give Chefland a new invention assuming that testing 1 gas takes 1 day.

## Constraints

• 1 â‰¤ T â‰¤ 10^5
• 1 â‰¤ N, K â‰¤ 10^9
• 0 â‰¤ p < N

Subtask #1 (100 points): Original constraints

Sample Input 1

``````4
10 5 5
10 6 5
10 4 5
10 8 5
``````

Sample Output 1

``````2
4
9
8
``````

Explanation

Test case 1: On the day 1 Chef will test gas numbered 0 and on the day 2 Chef will test gas numbered 5.

Test case 2: On the day 1 Chef will test gas numbered 0, on the day 2 Chef will test gas numbered 5, on the day 3 Chef will test gas numbered 1, and on the day 4 Chef will test gas numbered 6.

Test case 3: On the day 1 Chef will test gas numbered 0, on the day 2 Chef will test gas numbered 5, on the day 3 Chef will test gas numbered 1, on the day 4 Chef will test gas numbered 6, on the day 5 Chef will test gas numbered 2, on the day 6 Chef will test gas numbered 7, on the day 7 Chef will test gas numbered 3, on the day 8 Chef will test gas numbered 8, and on the day 9 Chef will test gas numbered 4.

Test case 4: On the day 1 Chef will test gas numbered 0, on the day 2 Chef will test gas numbered 5, on the day 3 Chef will test gas numbered 1, on the day 4 Chef will test gas numbered 6, on the day 5 Chef will test gas numbered 2, on the day 6 Chef will test gas numbered 7, on the day 7 Chef will test gas numbered 3, and on the day 8 Chef will test gas numbered 8.

## Solution – Chef and Bulb Invention

### Python

```T = int(input())
for _ in range(T):
n, p, k = map(int, input().split())
ans = 0

a = p%k - 1
b = ((n-1)//k)*k
b = n - 1 - b

if (a>b):
ans += (b+1)*((n-1)//k + 1) +(a-b)*((n-1)//k)
else:
ans += ((n-1)//k + 1)*(a+1)

for i in range(a+1, n, k):
ans += 1
if (i==p):
print(ans)
break```

### Java

Disclaimer: The above Problem (Chef and Bulb Invention) is generated by CodeChef but the Solution is Provided by CodingBroz. This tutorial is only for Educational and Learning Purpose.