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Problems

New Contest

New Contest

Time limit 0.5 seconds
Memory limit 64 MiB

Now, I made a contest for our coach’s - Etibar’s anniversary. I and he are really excited about it. There will be a total of S students in the contest. First N students in the final standings will be awarded.

He has a list (favorite students list) what cantains the best students in informatics Olympiad. His favorite students list contains M students. Though he is excited about the contest, he will enjoy it only if at least K of students from his favorite students list are awarded. He is wondering what are the chances of that happening. He needs your help. Tell him the probability that he will enjoy. It is known that each student has equal chance of being awarded.

Input data

First line contains the number of test cases T (1T100). In the next T lines, you are given 4 separated integers S, N, M and K (1 S1000, 1NS, 1MS, 0KM).

Output data

For each test case, output the required probability with 6 digits after floating point.

Examples

Input example #1
3
10 10 5 3
10 4 6 4
3 2 2 1
Output example #1
1.000000
0.071429
1.000000
Author Mahammad Valiyev
Source Local Contest #2 Qafqaz University by Mahammad Valiyev