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.

Input

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

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