A7946 | Road Map

There are $n$ cities in Berland. Each city has its index — an integer number from $1$ to $n$ . The capital has index $r_{1}$ . All the roads in Berland are two-way. The road system is such that there is exactly one path from the capital to each city, i.e. the road map looks like a tree. In Berland's chronicles the road map is kept in the following way: for each city $i$ , different from the capital, there is kept number $p_{i}$ — index of the last city on the way from the capital to $i$ .

Once the king of Berland Berl XXXIV decided to move the capital from city $r_{1}$ to city $r_{2}$ . Naturally, after this the old representation of the road map in Berland's chronicles became incorrect. Please, help the king find out a new representation of the road map in the way described above.

The first line contains three space-separated integers $n$ , $r_{1}$ , $r_{2}$ ( $2<=n<=5·10^{4},1<=r_{1}≠r_{2}<=n$ ) — amount of cities in Berland, index of the old capital and index of the new one, correspondingly.

The following line contains $n-1$ space-separated integers — the old representation of the road map. For each city, apart from $r_{1}$ , there is given integer $p_{i}$ — index of the last city on the way from the capital to city $i$ . All the cities are described in order of increasing indexes.

Output $n-1$ numbers — new representation of the road map in the same format.