Ant

Interview

Time limit0.15sMemory limit256 MB

Summary

Compute the position of an ant moving diagonally and reflecting off the walls of a w by h box after t hours.

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

Problem

A rectangular grid area is $w$ wide and $h$ tall. Its lower left corner is $(0, 0)$ and its upper right corner is $(w, h)$ . One ant sits at the point $(p, q)$ inside this area.

The ant starts moving at a constant speed in the up-right 45 degree direction. After one hour the ant that started at $(p, q)$ has moved to $(p+1, q+1)$ . When it hits a boundary while moving at that speed, it reflects and keeps the same speed.

The picture above shows the path of an ant that starts at $(4, 1)$ on a $6 \times 4$ grid. That ant is at $(6, 3)$ after 2 hours and at $(0, 1)$ after 8 hours. If the ant had started at $(5, 3)$ on the same grid, it would move to $(6, 4)$ , $(5, 3)$ , $(4, 2)$ , $(3, 1)$ hour by hour.

Compute and print the position $(x, y)$ of the ant $t$ hours after it starts at $(p, q)$ on a grid of size $w \times h$ . Assume the ant never tires and keeps the same speed.

$w$ and $h$ are natural numbers with $2 \le w, h \le 40000$ . The starting coordinates $p$ and $q$ are natural numbers with $0 < p < w$ and $0 < q < h$ . The time $t$ satisfies $1 \le t \le 200000000$ .

Input

The first line contains $w$ and $h$ separated by a space. The second line contains the starting coordinates $p$ and $q$ separated by a space. The third line contains the time $t$ the ant moves.

Output

Print $x$ and $y$ of the ant position $(x, y)$ after $t$ hours, separated by a space, on one line.

Examples5

Example 1
Input
```
6 4
4 1
8
```
Expected output
```
0 1
```
Example 2
Input
```
6 4
5 3
4
```
Expected output
```
3 1
```
Example 3
Input
```
6 4
4 1
2
```
Expected output
```
6 3
```
Example 4
Input
```
2 2
1 1
1
```
Expected output
```
2 2
```
Example 5
Input
```
5 7
4 6
1
```
Expected output
```
5 7
```