Codeforces Beta Round 34 (Div. 2) |
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Finished |

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D. Road Map

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThere 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.

Examples

Input

3 2 3

2 2

Output

2 3

Input

6 2 4

6 1 2 4 2

Output

6 4 1 4 2

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

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