Light The Bulb

Chef has a kitchen with a bulb and $N$ switches. The bulb will only light up if the $N$ switches are in a specific order, as given by a binary string $S$ of size $N$. In this binary string, `0` at the $i^{th}$ position represents that the $i^{th}$ switch is `OFF`, and `1` means that the switch is `ON`. Initially, Chef has the switches in the state represented by the binary string $T$ of length