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: Runtime Error)

####### 二項係数 C(n,k) mod pの計算 #######

MOD=10**9+7
FACT=[]
INV=[]

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

def calc_fact(n)
  FACT[0]=1
  INV[0]=pow(FACT[0],MOD-2)
  for i in 1..n
    FACT[i]=FACT[i-1]*i%MOD
    INV[i]=pow(FACT[i],MOD-2)
  end
end

def com(n,k)
  (FACT[n]*INV[n-k]%MOD)*INV[k]%MOD
end

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


H,W,A,B=gets.split.map(&:to_i)
calc_fact(H+W-2)
ans=0

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

puts ans%MOD