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 available 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)!


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


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 answer 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


hide comments
Rafail Loizou: 2021-02-21 22:46:44

@sherlock11 how is that true? 1/2 = 1 / 7 % 5 != (7^(5-2)) % 5 = 343 % 5 = 3. Do you mean something else?

adarshgaur: 2021-01-03 12:59:20

Thanks for this big time limit. XD

gxurav_07: 2020-07-26 18:55:23

How to understand how many queries are there

[NG]: As many as lines in testfile. In Python, iterate over stdin.readlines() or use try/except block to detect end of input.

Last edit: 2020-07-26 23:26:58
kaverikr: 2020-06-26 19:00:26

@morass can you please explain the mathematics for the computing the total number of combinations here, I am bit unclear on the concept behind the problem.

sherlock11: 2018-06-26 20:43:35

just remember 1/a%mod=(a^(mod-2))%mod if(mod==prime)

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
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

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