Let $T(m, n)$ be the number of the binomial coefficients $^iC_n$ that are divisible by $10$ for $n \le i \lt m$ ($i$, $m$ and $n$ are positive integers).
You are given that $T(10^9, 10^7-10) = 989697000$.
Find $T(10^{18}, 10^{12}-10)$.
Solution
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