You are given $3$ positive integers zero, one, and limit.

A binary array arr is considered stable if:

• The count of $0$s in arr is exactly zero.

• The count of $1$s in arr is exactly one.

• Every subarray of arr with a size strictly greater than limit contains both $0$ and $1$.

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

Constraints:

• $1 \leq$ zero, one, limit $\leq 200$

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