Jump Jump 2

Youngwoo the frog is on a stone bridge made of $n$ stones in a row. The stones are numbered $1$ to $n$ from the left, and stone $i$ has a single number $A_i$ written on it. From stone $i$ Youngwoo can jump exactly $A_i$ stones to the left or to the right, landing on stone $i - A_i$ or on stone $i + A_i$. He cannot jump to a position numbered below $1$ or above $n$.

Youngwoo starts on stone $s$. There is no limit on the number of jumps, and he may land on the same stone more than once. Call a stone visitable if Youngwoo can land on it after one or more jumps. The starting stone $s$ is visitable only when he can land back on it after at least one jump.

Count the visitable stones.

The first line contains the number of stones $n$ ($1 \le n \le 100000$).

The second line contains $A_1, A_2, \dots, A_n$, separated by spaces ($1 \le A_i \le 100000$).

The third line contains the starting position $s$ ($1 \le s \le n$).

Print the number of visitable stones on the first line.