Professor Mitrovoak has a rectangular image of his Slowbro, but wants to increase its resolution! The image file uses the Adjustable-Compression Photograph Composition (ACPC) image format, which allows its width $$$W$$$ and height $$$H$$$ to be stretched $$$K$$$ times without losing image details $$$(0 \le W, H, K \le 10^4)$$$. Professor Mitrovoak wants his image to have the maximum area possible.
In one stretch operation, either width $$$W$$$ or height $$$H$$$, but not both, can be increased by $$$1$$$. Professor Mitrovoak can stretch his image up to $$$K$$$ times.
Professor Mitrovoak wants the highest resolution possible. Given initial width $$$W$$$, initial height $$$H$$$, and limit $$$K$$$, determine the maximum area of the professor's picture!
The only line of input is three space-separated integers $$$W$$$, $$$H$$$, and $$$K$$$ ($$$0 \le W, H, K \le 10^4$$$).
Output a single integer: the maximum area an image can have after up to $$$K$$$ stretch operations.
3 7 3
42
0 10 0
0
0 0 5
6
In the first test case, the image has a width of $$$3$$$ pixels and a height of $$$7$$$ pixels, and up to $$$3$$$ stretch operations can be done. By stretching the width $$$3$$$ times, the final width is 6 and the final height is 7. Thus, the area of the image $$$(W*H=6*7)$$$ is $$$42$$$. This is the maximum area possible.
