Divisibility by 2^N

Consider an infinite numerical sequence defined as follows: A_1 = 1, A_2 = 12, ..., A_{10} = 12345678910, A_{11} = 1234567891011, and so on. The first term is $1$, and each subsequent term is formed by appending the decimal representation of its index to the end of the previous term's decimal value.

Given two integers, $M$ and $N$, your task is to find how many terms in this sequence, with an index not exceeding $M$, are divisible by 2^N without a remainder.