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: Accepted)

$fact = Array.new(2*10**6,0)
$fact[0] = 1
for i in 1..2*10**6-1
  $fact[i] = $fact[i-1]*(i+1)%(10**9+7)
end
$fact << 1
def exp(a,b)
  if b == 0
    1
  elsif b%2 == 0
    (exp(a,b/2)**2)%(10**9+7)
  else
    (a*exp(a,b-1))%(10**9+7)
  end
end
def combi(n,r)
  $fact[n-1]*exp($fact[n-r-1],10**9+5)*exp($fact[r-1],10**9+5)%(10**9+7)
end
h,w,a,b = gets.chomp.split(" ").map(&:to_i)
ans = 0
if a > h/2
  for i in 0..h-a-1
    ans += combi(i+b-1,b-1)*combi(h+w-i-b-2,w-b-1)
  end
else
  ans += combi(h+w-2,h-1)
  for i in 0..a-1
    ans -= combi(h-a+i+b-1,b-1)*combi(a-i+w-b-2,w-b-1)
  end
end
puts ans%(10**9+7)