Function Run Fun

Time Limit: 2 Seconds
Memory Limit: 65536 KB

We all love recursion! Don't we?

Consider a three-parameter recursive function w(a, b, c):

if a <= 0 or b <= 0 or c <= 0, then w(a, b, c) returns:

1

if a > 20 or b > 20 or c > 20, then w(a, b, c) returns:

w(20, 20, 20)

if a < b and b < c, then w(a, b, c) returns:

w(a, b, c-1) + w(a, b-1, c-1) - w(a, b-1, c)

otherwise it returns:

w(a-1, b, c) + w(a-1, b-1, c) + w(a-1, b, c-1) - w(a-1, b-1, c-1)

This is an easy function to implement. The problem is, if implemented directly,
for moderate values of a, b and c (for example, a = 15, b = 15, c = 15), the
program takes hours to run because of the massive recursion.

**Input**

The input for your program will be a series of integer triples, one per line,
until the end-of-file flag of -1 -1 -1. Using the above technique, you are to
calculate w(a, b, c) efficiently and print the result. For example:

1 1 1

2 2 2

10 4 6

50 50 50

-1 7 18

-1 -1 -1

**Output**

Print the value for w(a,b,c) for each triple, like this:

w(1, 1, 1) = 2

w(2, 2, 2) = 4

w(10, 4, 6) = 523

w(50, 50, 50) = 1048576

w(-1, 7, 18) = 1

Source:

**Pacific Northwest 1999**
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