ADATEAMS - Ada and Teams


Ada the Ladybug is a well known mathematician. Next week she is going to represent her school in Mathematic Olympiad. There are many schools participating and each of them has many students. Anyway only some of the students and only some of the schools will be availible to participate in the Olympiad. Question is, how many combinations of students can participate in the Olympiad?

More specifically: There are N schools from which exactly A will participate. Moreover there are B students in each school and exactly D of them will participate in the Olympiad.

Ada could count it herself. But this process takes too much time and the limits for schools and students are changing every moment so she has decided to make a program for it (in fact she has decided that you will make the program for her)!

Input

The input contains up to 104 lines, each containing four integers N,A,B,D, 1 ≤ A ≤ N ≤ 106,1 ≤ D ≤ B ≤ 106

Output

For each line print the number of combination of students, which can participate in the Olympiad. All students and universities are distinguishable, but their order doesn't matter.

Since the anwer might be huge, print it modulo 109+7 (1000000007)

Example Input

2 1 2 2
2 2 2 1
2 1 2 1
4 3 3 2
4 2 1 1
10 4 12 7
50 30 44 20

Example Output

2
4
4
108
6
625817778
154746653

hide comments
Vipul Srivastava: 2017-04-30 15:46:37

Last edit: 2017-04-30 15:48:53
rrm_2016: 2016-11-22 20:53:41

@morass: can u please check my solution...i tried all possible test cases and i am getting right answer ... i think i m doing something wrong with the input format as this is the first time i am trying this kind of input format...please check

Last edit: 2016-11-22 21:05:00
rrm_2016: 2016-11-21 22:27:51

Last edit: 2016-11-22 00:22:11
morass: 2016-09-25 14:22:34

@vikramsr: Good day to you. Problem is, that you update "f" every time you call "C", making the function O(N). Anyway as you can see, you can precalculate "f" (since it is argument independent) making your "C" function O(log(N)) :) Good Luck!

vikramsr: 2016-09-25 09:58:04

can u plz check my solution..

morass: 2016-09-17 07:50:12

@Harsh Rumalwala: Good day to you... in my opinion changing "si(n)" to "~si(n)" shall be enough :) [bad EOF check :P]

Harsh Rumalwala: 2016-09-17 05:05:43

@morass : Thanks for pointing out modified , it was a bad EOF check..

Last edit: 2016-09-17 12:42:55
hanstan: 2016-09-13 14:12:36

Nice time limit :P

Piyush Kumar: 2016-09-08 18:10:54

Thanks for the generous time limit :)


Added by:Morass
Date:2016-09-05
Time limit:4s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64 GOSU