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: Wrong Answer)

####### 二項係数 C(n,k) mod pの計算 #######

MOD=10**9+7

## a**b mod p by 繰り返し二乗法 ##
def pow(a,b)
  return 1 if b==0
  return a*pow(a,b-1)%MOD if b%2==1
  return pow(a**2%MOD,b/2)
end

## n! mod p ##
def fact(n)
  ret=1
  n.times do |i|
    ret=ret*(i+1)%MOD
  end
  ret
end

## a**(-1) mod p ##
def inv(n)
  pow(n,MOD-2)%MOD
end

## C(n,k) mod p ##
def com(n,k)
  (fact(n)*inv(fact(k)))%MOD*inv(fact(n-k))%MOD
end

## C(n,k) mod p (n>>>k version) ##
def frac(n,k)
  a=1
  b=1
  k.times do |i|
    b*=i+1
    b%=MOD
  end
  k.times do |i|
    j=i+1
    a*=n-i
    a%=MOD
  end
  a*inv(b)%MOD
end

##########################################


H,W,A,B=gets.split.map(&:to_i)
ans=0

for i in 1..H-A do
  ans+=com(B+i-1,B)*com(H-i+W-B-2,H-i)%MOD
  ans+=com(B+i-1,B)*com(A-1+W-B-1,A-1)%MOD  if i==H-A
end

puts ans%MOD