AE Hash Function

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Chef Ash and Chef Elsh invented a new hash function! Their hash function will map a binary string consisting of characters 'A' and 'E' into an integer called the hash value of the string.
The pseudocode of the hash function is as below. hash(S) is the hash value of a binary string S. S denotes the length of S.
function hash(S): result = number of characters 'A' in S if S > 1: (S1, S2) = split(S) result = result + max(hash(S1), hash(S2)) end if return result end function
The function split in the above pseudocode takes a binary string S as the parameter and returns a pair of binary strings (S1, S2) such that:
 S1 <= S2.
 The difference of S1 and S2 is at most 1.
 The concatenation of S1 and S2 (in that order) is S.
For example, split("AAAEE") returns ("AA", "AEE"), whereas split("AEAEAE") returns ("AEA", "EAE").
You doubt that this hash function have good distribution of different hash values. So, you wonder how many different binary strings consisting of A 'A' characters and E 'E' characters that have hash value of V.
Input
The first line contains a single integer T, the number of test cases. T test cases follow. Each testcase consists of a single line consisting of three integers A, E, and V.
Output
For each test case, output a single line consisting the number of different binary strings satisfying the rule, modulo 1000000007.
Constraints
 1 ≤ T ≤ 1000
 0 ≤ A ≤ 50
 0 ≤ E ≤ 50
 0 ≤ V ≤ 1000
Example
Input: 4 0 0 0 1 0 1 3 2 6 4 2 8 Output: 1 1 3 4
Explanation
For the last test case, the solutions are:
 AAEAAE
 AEAAAE
 AAEAEA
 AEAAEA
Author:  fushar 
Tester:  gamabunta 
Editorial  http://discuss.codechef.com/problems/AEHASH 
Tags  easy, fushar, july11 
Date Added:  11062011 
Time Limit:  0.286613 sec 
Source Limit:  50000 Bytes 
Languages:  C, CPP14, JAVA, PYTH, PYTH 3.5, CS2, PAS fpc, PAS gpc, RUBY, PHP, GO, NODEJS, HASK, SCALA, D, PERL, FORT, WSPC, ADA, CAML, ICK, BF, ASM, CLPS, PRLG, ICON, SCM qobi, PIKE, ST, NICE, LUA, BASH, NEM, LISP sbcl, LISP clisp, SCM guile, JS, ERL, TCL, PERL6, TEXT, CLOJ, FS 
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