Given three positive integers zero, one, and limit.

A binary array arr is considered stable if:

• The number of occurrences of $0$ in arr is exactly zero.

• The number of occurrences of $1$ in arr is exactly one.

• Every contiguous subarray of arr with a length strictly greater than limit contains at least one $0$ and at least one $1$.

Return the total number of stable binary arrays. Since the answer can be very large, return it modulo $10^9 + 7$.

Constraints:

• $1 \leq$ zero, one, limit $\leq 1000$

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