1444 - Number of Ways of Cutting a Pizza\.

Hard

Given a rectangular pizza represented as a rows x cols matrix containing the following characters: 'A' (an apple) and '.' (empty cell) and given the integer k. You have to cut the pizza into k pieces using k-1 cuts.

For each cut you choose the direction: vertical or horizontal, then you choose a cut position at the cell boundary and cut the pizza into two pieces. If you cut the pizza vertically, give the left part of the pizza to a person. If you cut the pizza horizontally, give the upper part of the pizza to a person. Give the last piece of pizza to the last person.

_Return the number of ways of cutting the pizza such that each piece contains at least one apple. _Since the answer can be a huge number, return this modulo 10^9 + 7.

Example 1:

Input: pizza = "A..","AAA","...", k = 3

Output: 3

Explanation: The figure above shows the three ways to cut the pizza. Note that pieces must contain at least one apple.

Example 2:

Input: pizza = "A..","AA.","...", k = 3

Output: 1

Example 3:

Input: pizza = "A..","A..","...", k = 1

Output: 1

Constraints:

• 1 <= rows, cols <= 50

• rows == pizza.length

• cols == pizza[i].length

• 1 <= k <= 10

• pizza consists of characters 'A' and '.' only.