# Codingame: Simultaneous Ages

## Goal

`Y`years ago, Person A was

`M`times older than Person B. Currently, Person A is older than Person B by

`N`years. What are their ages now?

Input

**Line 1:**3 integers:

`N`

`M`

`Y`

Output

**Line 1:**

`A`

`B`, Person A and B's age respectively.

Constraints

0 <

0 <

`B`<`A`< 100,0000 <

`N`,`M`,`Y`< 100,000## Solution

The current situation is that \(A = B + N\). \(Y\) years ago, the situation was \(A = B \cdot M\), which means that:

\[\begin{array}{rrl}& A-Y =& (B - Y) M\\\Leftrightarrow & B + N - Y =& B M - Y M\\\Leftrightarrow & B =& \frac{Y - Y M - N}{1 - M}\\\Leftrightarrow & B =& Y+\frac{ N}{M - 1}\end{array}\]

Finally, \(B\) can be used for the first formula. Implementing the routine in JavaScript then looks as follows:

var inputs = readline().split(' '); var N = +inputs[0]; var M = +inputs[1]; var Y = +inputs[2]; var B = Y + N / (M - 1); var A = B + N; print(A + " " + B);