Balls

Interview

Time limit2sMemory limit1024 MB

Summary

Given two balls with integer positions and velocities that swap velocities on each elastic collision, print each ball's position and velocity at time T.

Level: Easy3 of 10
Topics: Math, Simulation
Solved: No attempts yet

Statement

A wicked wizard named Liahi placed two infinitely small balls of equal mass at different points with integer coordinates $x_1$ and $x_2$ on the real axis. At time $0$ he gave the $i$ -th ball a velocity $v_i$ and watched them move. The collisions are perfectly elastic. Because the masses are equal, after a collision each ball moves with the velocity of the other ball and takes over its direction of motion.

The wizard wants a program that prints the state of both balls at time $T$ . If the program is wrong, he will put you inside one of these balls.

Input

The first line contains $x_1$ and $v_1$ . The second line contains $x_2$ and $v_2$ . The third line contains $T$ . All numbers are integers with absolute values not exceeding $10^4$ .

Output

Print two lines. The first line contains the position and velocity of the first ball at time $T$ . The second line contains the position and velocity of the second ball at time $T$ . Round every value to the nearest integer. Separate the numbers in each line with a space. The coordinates of the balls are guaranteed to differ at time $0$ and at time $T$ .

Examples2

Example 1
Input
```
1 2
2 2
5
```
Expected output
```
11 2
12 2
```
Example 2
Input
```
8 2
12 -2
10
```
Expected output
```
-8 -2
28 2
```