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Problem
A tree with `n` nodes numbered from `1` to `n` is represented by
the parent array `t`, where `t[i]` is the parent of node `i`, and
`t[i] = 0` means that node `i` is the root of the tree.
An additional natural number `x` with `1 <= x <= n` is also read. Print
the path from node `x` to the root, starting with `x` and ending with
the root, following edges upward.
Input format
Input
input.txt
The first line contains two natural numbers `n` and `x`, separated by a space. The second line contains the `n` values of the parent array, separated by spaces. - `1 <= n <= 100` - `1 <= x <= n` - the array describes a valid tree - if `x` is the root, print only `x`
Output format
Output
output.txt
The program prints the indices of the nodes on the path from `x` to the root, separated by spaces, in order: `x`, parent of `x`, grandparent of `x`, ..., root.
Example
input
7 1 2 4 4 0 4 5 5
output
1 2 4
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Sample cases (from the problem)
Sample Case 1
Input
7 1 2 4 4 0 4 5 5
Expected output
1 2 4
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