## B - Good Predictions

Having arrived at the ACM-ICPC contest site in a fun-filled mood, The Team continues their important pre-contest preparations. Specifically, every world-class team knows the importance of making predictions about their upcoming submissions.

The Team knows that they'll get plenty of AC (Accepted) submissions, and they find those quite boring by now. As such, they'll focus on their incorrect ones. From their vast experience, The Team knows that they'll only get exactly `N` (1 ≤ `N` ≤ 300) submissions wrong throughout the upcoming contest - in fact, they predict that, of those, exactly `W` (0 ≤ W ≤ 100) will get WA (Wrong Answer), `T` (0 ≤ `T` ≤ 100) will get TLE (Time Limit Exceeded), and the remaining `R` (0 ≤ `R` ≤ 100) will get RE (Runtime Error). Note that `W` + `T` + `R` = `N`.

Assuming that their predictions will certainly be correct, the members of The Team are wondering in how many ways that might occur. In other words, how many different ordered combinations of `N` incorrect results (each being WA, TLE, or RE) exist which satisfy their predictions? Since The Team doesn't make many mistakes, surely you can calculate this value, right? However, since it can get quite large for you, compute it modulo (10^{9} + 7).

### Input

4 integers, `N`, `W`, `T`, and `R`

### Output

1 integer, the number of valid ordered combinations of submission results, modulo (10^{9} + 7).

### Sample Input

3 2 1 0

### Sample Output

3

### Explanation of Sample

Out of 3 submissions, two are WA, while the third is TLE. The following 3 ordered combinations are then possible:

WA, WA, TLE

WA, TLE, WA

or

TLE, WA, WA

The answer is then 3 modulo (10^{9} + 7) = 3.

All Submissions

Best Solutions

**Point Value:** 10

**Time Limit:** 4.00s

**Memory Limit:** 64M

**Added:** Jun 01, 2012

**Author:** SourSpinach

**Languages Allowed:**

C++03, PAS, C, HASK, ASM, RUBY, PYTH2, JAVA, TEXT, PHP, SCM, CAML, PERL, C#, C++11, PYTH3

## Comments (Search)

Danielon Jun 03, 2012 - 2:21:27 am UTC There may be an issue with test case #5jargonon Jun 03, 2012 - 2:46:13 am UTC Re: There may be an issue with test case #5The case should be:

as opposed to:

However, mathematical solutions, in exploiting bignums, should probably be disallowed.

Alexon Jun 03, 2012 - 3:24:52 am UTC Re: Re: There may be an issue with test case #5SourSpinachon Jun 03, 2012 - 7:40:33 am UTC Re: Re: There may be an issue with test case #5Thanks for pointing this out. The data's been fixed, and all solutions rejudged.

I won't disallow any solutions - people can use math if they want, I personally find that more difficult anyway.

bbi5291on Jun 04, 2012 - 6:11:55 am UTC Re: Re: There may be an issue with test case #5