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 Python (3.4.3) (judge verdict: Accepted)

iH,iW,iA,iB = [int(x) for x in input().split()]
iD = 10**9+7 #法

#初等整数論勉強して解説通りキッチリ実装したった

#二分累乗法 iDを法として
def fBiPow(iX,iN,iD):
    iY = 1
    while iN > 0:
        if iN % 2 == 0:
            iX = iX * iX % iD
            iN = iN // 2
        else:
            iY = iX * iY % iD
            iN = iN - 1
    return iY

#nCr = n!/r!(n-r)!
#ループ回すだけ版や
def fFr(iX,iR=1):
    if iR == 0 or iX == 0:
        return 1
    else :
        iRet = 1
        for i in range(iR,iX+1):
            iRet *= i
        return iRet

def fnCr(iN,iR):
    if iR == 0:
        return 1
    else:
        return fFr(iN,iR+1) // fFr(iN-iR)

#階乗(iDを法とした)の配列
aM = [1]*(iH+iW-1)
for i in range(1,iH+iW-1):
    aM[i]=aM[i-1]*i %iD
#各階乗のiDを法とした逆元の配列
aInvM = [1]*(iH+iW-1)
aInvM[iH+iW-2] = fBiPow(aM[iH+iW-2],iD-2,iD)
for i in range(iH+iW-2,0,-1):
    aInvM[i-1]=aInvM[i]*i % iD

iRet = 0
for iL in range(0,iH-iA):
    #iRet += (fnCr(iL+iB-1,iL) * fnCr(iW-iB+iH-iL-2,iW-iB-1))%iD
    iRet += (aM[iL+iB-1]*aInvM[iL]*aInvM[iB-1]) % iD * (aM[iW-iB+iH-iL-2]*aInvM[iW-iB-1]*aInvM[iH-iL-1])%iD
    iRet %= iD
iRet %= iD
print(iRet)