Matrix Reachability

You are given a directed graph with vertices numbered from $1$ to $n$. The graph is described by its adjacency matrix: the entry in row $i$ and column $j$ is 1 if there is a directed edge from vertex $i$ to vertex $j$, and 0 otherwise.

Starting at vertex $s$, determine every vertex that can be reached by following zero or more directed edges.

Input

The first line contains two integers $n$ and $s$, the number of vertices and the starting vertex.

The next $n$ lines each contain $n$ integers. The $j$-th integer on the $i$-th of these lines is the adjacency matrix entry for the directed edge from vertex $i$ to vertex $j$.

Output

Output one line containing all reachable vertices in increasing order, separated by spaces.

Constraints

• $1 \le n \le 500$
• $1 \le s \le n$
• Each matrix entry is either 0 or 1.

Example 1

4 1
0 1 1 0
0 0 0 1
0 0 0 0
0 0 1 0

1 2 3 4

Explanation

From vertex $1$, we can directly reach vertices $2$ and $3$. From vertex $2$, we can reach vertex $4$, so all vertices are reachable.

Example 2

5 3
0 0 0 0 0
1 0 0 0 0
0 0 0 1 0
0 0 0 0 1
0 0 0 0 0

3 4 5

Explanation

Starting at vertex $3$, the only new vertices reachable are $4$ and then $5$.