Background

Compressed Towel.

What, this is not an open contest; this is a compressed towel that becomes bigger and taller when it meets water.

Problem Description

This is a magical compressed towel that can grow without limit.

The compressed towel’s initial length, width, and height are $a, b, h$ centimeters. It meets water $k$ times. Each time it meets water, its length, width, and height each increase by $1$ centimeter. Please output the final volume of the compressed towel, in cubic centimeters.

However, someone thinks this problem is too easy, and being lazy, they threw it to you, so you need to solve it.

Input Format

Four numbers: $a, b, h, k$.

Output Format

Output one number as the answer. Since the answer may be too large, output its value $\bmod~988444333$.

Please note the modulus used in this problem.

1 1 4 5

324

100 100 100 0

1000000

114 51 419 198

47933496

Hint

Sample Explanation $1$

We can compute $(1+5)\times(1+5)\times(4+5)=6\times6\times9=324$.

Sample Explanation $2$

Please note that the compressed towel may also not meet water.

Constraints

For $100\%$ of the testdata, $1\leq a,b,h\leq 500$, $0\leq k\leq 500$.

Translated by ChatGPT 5