Count how many binary arrays can be formed with fixed numbers of 0s and 1s while satisfying a stability condition on consecutive equal values.
Given two integers representing the number of 0s and 1s available, count how many binary arrays can be formed using exactly those values such that the array remains stable under the problem's constraint on runs of equal elements. Return the total number of valid arrays.
A valid solution should focus on counting arrangements rather than enumerating all possibilities explicitly.
Input Format
- Two integers describing the available counts of 0s and 1s.
- An additional integer describing the stability limit or constraint parameter, if applicable to the specific version of the problem.
The exact input format follows the platform's function signature.
Output Format
- Return the number of stable binary arrays that can be formed.
- If the answer is large, return it modulo the problem-specified value when required.
Constraints
- The array must use exactly the given counts of 0s and 1s.
- The stability condition restricts how consecutive equal values may appear.
- Time-efficient counting is expected; brute-force generation is not feasible for large counts.
Example 1
Input
zero = 1, one = 1, limit = 1
Output
2
Explanation
The valid arrays are [0,1] and [1,0].
Example 2
Input
zero = 2, one = 1, limit = 2
Output
3
Explanation
The valid arrays are [0,0,1], [0,1,0], and [1,0,0].
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