100423: [AtCoder]ABC042 D - Iroha and a Grid

Memory Limit:256 MB Time Limit:2 S
Judge Style:Text Compare Creator:
Submit:0 Solved:0

Description

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

Input

题意翻译

**题意:** 有一个$H*W$ 的矩阵, 现在你正位于左上角的格子, 并且你只能向右移动或向下移动, 不幸的是, 矩阵的左下角$A*B$ 的地方被划为了禁区, 即你不能在此行走, 那么现在你有多少种方法从左上角走到右下角的格子呢? **输入:** 一行四个整数$H,W,A,B$ **输出:** 方案数,由于方案数很大,请对$10^9+7$ 取模 感谢@凌幽 提供的翻译

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