if N=3 k=10
is 011 valid(i mean may the valid number start with 0?)

011 is actually 11 so no.
a small hint:

first, lets consider A ∈ { 1, 2, 3, ..., k-1}

the numbers that are invalid should look like this: A00, where A can take any value from those above. no matter what values do N and K take, your numbers must always start with A. if not, then u have a number with N-1 elements. hope this helps.

this reply was quite late :-)