Problem 322

Binomial coefficients divisible by 10

Let T(m, n) be the number of the binomial coefficients ⁱC_n that are divisible by 10 for n ≤ i < m(i, m and n are positive integers).
You are given that T(10⁹, 10⁷-10) = 989697000.

Find T(10¹⁸, 10¹²-10).

能被10整除的二项式系数

记T(m, n)是所有能被10整除的二项式系数ⁱC_n的数目，其中n ≤ i < m（i、m、n均为正整数）。
已知T(10⁹, 10⁷-10) = 989697000。

求T(10¹⁸, 10¹²-10)。