BigFunc | Topcoder Archive

Problem Statement

Your math teacher has given you the following mystery functions:

           {            n                  if m = 0
f(m,n) =   {            0                  if n = 0
           { n*f(m-1,n) - g(m-1,n-1)	   otherwise

           {        0                 if y = 0
g(x,y) =   {  
           { f(x,y) + g(x,y-1)        otherwise

Given m and n your function will return the value of f.

Definition

Class:: BigFunc
Method:: value
Parameters:: int, int
Returns:: long
Method signature:: long value(int m, int n)
(be sure your method is public)

Notes

It should be clear from the above recurrences that the function will always converge to a value. i.e. it will not go into an infinite recurrence.

Constraints

m will be between 0 and 100 inclusive
n will be between 0 and 100 inclusive
The return value will be between 0 and 2^63-1 inclusive.

Examples

```
10
```
```
1
```
```
Returns: 1
```
```
1
```
```
4
```
```
Returns: 10
```
```
10
```
```
10
```
```
Returns: 14914341925
```
```
20
```
```
8
```
```
Returns: 1236466399775623332
```

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