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B - Takahashi's Secret

Score : $200$ points

Problem Statement

Takahashi has $N$ friends. They have nicknames: Friend $1$, Friend $2$, $\ldots$, Friend $N$.

One day, Takahashi accidentally let one of his friends, Friend $X$, learn his shameful secret.
For each $i = 1, 2, \ldots, N$, when Friend $i$ learns the secret, he/she will share it with Friend $A_i$, if Friend $A_i$ has not already learned it.

How many of Takahashi's friends will learn the secret in the end?

Constraints

• $2 \leq N \leq 10^5$
• $1 \leq X \leq N$
• $1 \leq A_i \leq N$
• $A_i \neq i$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $X$

$A_1$ $A_2$ $\cdots$ $A_N$

Output

Print the answer.

4 2
3 1 1 2

3

Takahashi's secret will be learned by Friend $1$, Friend $2$, and Friend $3$, as follows.

• One day, Takahashi let Friend $2$ learn the secret.
• Friend $2$ shares it with Friend $1$.
• Friend $1$ shares it with Friend $3$.

In the end, three of his friends learn the secret, so we print $3$.

20 12
7 11 10 1 7 20 14 2 17 3 2 5 19 20 8 14 18 2 10 10

7