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 Fortran (gfortran v4.8.4) (judge verdict: Accepted)

program main
  implicit none
  integer(8),parameter::M=1000000007
  integer(8) h,w,a,b,i,asize
  integer(8),allocatable::fact(:),invf(:)
  integer(16)::i16=0

  read*,h,w,a,b
  asize=h+w
  allocate(fact(asize+1),invf(asize+1))

  fact(1:2)=1
  do i=1,asize
     fact(i+1)=mod(fact(i)*i,M)
  enddo
  invf(asize+1)=powmod(fact(asize+1))
  do i=asize,1,-1
     invf(i)=mod(invf(i+1)*i,M)
  enddo
  
  print*,mod(dot_product(&
       i16+mod(fact(h-a+b:h-a+w-1)*invf(b+1:w),M),mod(fact(w-b+a-1:a:-1)*invf(w-b:1:-1),M))*mod(invf(h-a)*invf(a),M),M)

  !end program main
contains
  function powmod(t) result(r)
    integer(8),intent(in)::t
    integer(8)x,i,r
    i=M-2
    x=t
    r=1
    do
       if ( i .eq. 0 ) exit
       if ( iand(i,1).eq.1 )then
          r=mod(r*x,M)
       endif
       x=mod(x*x,M)
       i=ishft(i,-1)
    end do
  end function powmod
end program main