2466 - Count Ways To Build Good Strings.

Medium

Given the integers zero, one, low, and high, we can construct a string by starting with an empty string, and then at each step perform either of the following:

• Append the character '0' zero times.

• Append the character '1' one times.

This can be performed any number of times.

A good string is a string constructed by the above process having a length between low and high ( inclusive ).

Return the number of different good strings that can be constructed satisfying these properties. Since the answer can be large, return it modulo <code>10⁹ + 7</code>.

Example 1:

Input: low = 3, high = 3, zero = 1, one = 1

Output: 8

Explanation:

One possible valid good string is "011".

It can be constructed as follows: "" -> "0" -> "01" -> "011".

All binary strings from "000" to "111" are good strings in this example.

Example 2:

Input: low = 2, high = 3, zero = 1, one = 2

Output: 5

Explanation: The good strings are "00", "11", "000", "110", and "011".

Constraints:

• <code>1 <= low <= high <= 10⁵</code>

• 1 <= zero, one <= low