Kata

Consider a pyramid made up of blocks. Each layer of the pyramid is a rectangle of blocks, and the dimensions of these rectangles increment as you descend the pyramid. So, if a layer is a 3x6 rectangle of blocks, then the next layer will be a 4x7 rectangle of blocks. A 1x10 layer will be on top of a 2x11 layer on top of a 3x12 layer, and so on.

Task

Given the dimensions of a pyramid's topmost layer w,l, and its height h (aka the number of layers), return the total number of blocks in the pyramid.

Examples

num_blocks(1, 1, 2) will return 5. This pyramid starts with a 1x1 layer and has 2 layers total. So, there is 1 block in the first layer, and 2x2=4 blocks in the second. Thus, 5 is the total number of blocks.

num_blocks(2, 4, 3) will return 47. This pyramid has 3 layers: 2x4, 3x5, and 4x6. So, there are 47 blocks total.

Notes

All parameters will always be postive nonzero integers.

Efficiency is important. There will be:

• 100 'small' cases with w, l, and h below 20.
• 100 'big' cases with w, l, and h between 1e9 and 1e10.