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)


@h,@w,@a,@b = gets.chomp.split(' ').map(&:to_i)

# x+1,y+1にいるパターン
# x    , y + 1
# x + 1, y

@memo = {}
def dfs(x,y)
  return 1 if x == @w and y == @h
  return 0 if @h - @a < y and x <= @b
  ret = []
  if x != @w
    ret << [x+1,y]
  end
  if y != @h
    ret << [x,y+1]
  end
  ret
end

count = 0
que = [[1,1]]
while (q = que.pop)
  a = dfs(*q)
  if a.instance_of? Array
    que+= a
  else
    count += a
  end
end

puts (count % (10**9 + 7))