A positive integer with k (decimal) digits is called balanced if its first ^k/₂ digits sum to the same value as its last ^k/₂ digits, where x, pronounced ceiling of x, is the smallest integer x, thus π = 4 and 5 = 5.

So, for example, all palindromes are balanced, as is 13722.

Let T(n) be the sum of all balanced numbers less than 10ⁿ.
Thus: T(1) = 45, T(2) = 540 and T(5) = 334795890.

Find T(47) mod 3¹⁵