A8908 | Find Marble

Petya and Vasya are playing a game. Petya's got $n$ non-transparent glasses, standing in a row. The glasses' positions are indexed with integers from $1$ to $n$ from left to right. Note that the positions are indexed but the glasses are not.

First Petya puts a marble under the glass in position $s$ . Then he performs some (possibly zero) shuffling operations. One shuffling operation means moving the glass from the first position to position $p_{1}$ , the glass from the second position to position $p_{2}$ and so on. That is, a glass goes from position $i$ to position $p_{i}$ . Consider all glasses are moving simultaneously during one shuffling operation. When the glasses are shuffled, the marble doesn't travel from one glass to another: it moves together with the glass it was initially been put in.

After all shuffling operations Petya shows Vasya that the ball has moved to position $t$ . Vasya's task is to say what minimum number of shuffling operations Petya has performed or determine that Petya has made a mistake and the marble could not have got from position $s$ to position $t$ .

The first line contains three integers: $n,s,t\ (1<=n<=10^{5}; 1<=s,t<=n)$ — the number of glasses, the ball's initial and final position. The second line contains $n$ space-separated integers: $p_{1},p_{2},...,p_{n}\ (1<=p_{i}<=n)$ — the shuffling operation parameters. It is guaranteed that all $p_{i}$ 's are distinct.

Note that $s$ can equal $t$ .

If the marble can move from position $s$ to position $t$ , then print on a single line a non-negative integer — the minimum number of shuffling operations, needed to get the marble to position $t$ . If it is impossible, print number -1.