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Maximum Multiplication

Limits 1s, 512 MB

You will be given three integers a, b and k. You can perform one of the following two operations maximum k times.

  • Increase the value of a by one.
  • Increase the value of b by one.

You have to maximize the value of a×b after performing all the operations.

Input

The first line of the input contains three integers a, b and k (1 ≤ a, b, k ≤ 1000).

Output

Print the maximum value of a×b after performing the above operations maximum k times.

Samples

InputOutput
2 4 3
20

In this case, we can perform the increase operations on the value a by k times. So after all the operations are done a will become 5 and b will be 4. Our final result is 4×5 = 20. This is the maximum possible answer that we can get in optimal strategy.

InputOutput
20 30 16
1089
InputOutput
50 55 6
3080
InputOutput
5 9 3
72


    Discussion
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    90% Solution Ratio

    mahfuj02 Earliest, 6M ago

    mahfuj02 Fastest, 0.0s

    piash18 Lightest, 0 B

    touhidur Shortest, 80B

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