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:
'0' zero times.'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 109 + 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 <= 1051 <= zero, one <= low