Problem:
Score : 400 points

Problem Statement

We have a large square grid with H rows and W columns.
Iroha is now standing in the top-left cell.
She will repeat going right or down to the adjacent cell, until she reaches the bottom-right cell.

However, she cannot enter the cells in the intersection of the bottom A rows and the leftmost B columns. (That is, there are A×B forbidden cells.) There is no restriction on entering the other cells.

Find the number of ways she can travel to the bottom-right cell.

Since this number can be extremely large, print the number modulo 10^9+7.

Constraints

1 ≦ H, W ≦ 100,000

1 ≦ A < H

1 ≦ B < W

Input

The input is given from Standard Input in the following format:

H W A B

Output

Print the number of ways she can travel to the bottom-right cell, modulo 10^9+7.

Sample Input 1

2 3 1 1

Sample Output 1

2

We have a 2×3 grid, but entering the bottom-left cell is forbidden. The number of ways to travel is two: "Right, Right, Down" and "Right, Down, Right".

Sample Input 2

10 7 3 4

Sample Output 2

3570

There are 12 forbidden cells.

Sample Input 3

100000 100000 99999 99999

Sample Output 3

1

Sample Input 4

100000 100000 44444 55555

Sample Output 4

738162020

Solution in Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

# Your code here!


def combi(a,b)
    ans=1
    i=1
    j=a
    b.times{
       ans=ans*j/i 
       i+=1
       j-=1
        
    }
    return ans
end

answer=0
a,b,c,d=gets.split
a=a.to_i
b=b.to_i
c=c.to_i
d=d.to_i

ll=[a-c,b-d].min
i=0
aa=a-c-1
bb=d
cc=b-1-d
dd=c
ll.times{
answer+=combi(aa+bb,bb)*combi(cc+dd,dd)
answer=answer%1000000007

aa-=1
bb+=1
cc-=1
dd+=1
    
}

p answer