Numismatics

There are $N$ slots in a row, numbered from $1$ to $N$ from left to right respectively. Each slot is either empty or has a coin in it. It is given that the $N^{th}$ slot is **always empty**. Whenever Chef is standing in $i^{th}$ slot, where $i^{th}$ slot is empty, he collects all the consecutive coins to his right, ie. he collects all the coins from $(i+1)^{th}$ to $(i+k)^{th}$ slot, assuming eac