FAIRSHARE - Editorial

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PROBLEM LINK:

Practice
Contest: Division 1
Contest: Division 2
Contest: Division 3
Contest: Division 4

Author: raysh_07
Tester: apoorv_me
Editorialist: iceknight1093

DIFFICULTY:

TBD

PREREQUISITES:

None

PROBLEM:

You and K friends eat at a restaurant, with the total cost being N.
This is divided equally among the group, and everyone pays you back; however, if they owe you x they pay you x rounded down to the nearest integer instead.

What’s your total expenditure?

EXPLANATION:

Note that the description of what your friends pay, i.e rounding down to the nearest integer, is exactly the floor function.
For a real number x, this will be denoted \left\lfloor x \right\rfloor.

Including you, the group has K+1 people.
So, splitting the cost equally among everyone, each person owes Rs. \frac{N}{K+1}

Of this, you pay N, then your K friends each pay you back Rs. \left\lfloor \frac{N}{K+1} \right\rfloor.
So, your total expenditure is exactly

N - K\cdot \left\lfloor \frac{N}{K+1} \right\rfloor

TIME COMPLEXITY:

\mathcal{O}(1) per testcase.

CODE:

Editorialist's code (Python) 
for _ in range(int(input())):
    n, k = map(int, input().split())
    print(n - k*(n//(k+1)))