"""
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 10^9 + 7.

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:
1 <= low <= high <= 10^5
1 <= zero, one <= low

hints:
1 Calculate the number of good strings with length less or equal to some constant x.
2 Apply dynamic programming using the group size of consecutive zeros and ones.
"""

class CountWaysToBuildGoodStrings:
    def countGoodStrings(self, low: int, high: int, zero: int, one: int) -> int:
        res = 0
        MOD = 10 ** 9 + 7
        dp = [0] * (high + 1)
        dp[0] = 1
        for i in range(1, high + 1):
            if i >= zero:
                dp[i] = (dp[i] + dp[i - zero]) % MOD
            if i >= one:
                dp[i] = (dp[i] + dp[i - one]) % MOD
            if i >= low:
                res = (res + dp[i]) % MOD
        return res