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

Input

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

Output

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

Input

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

Output

3 4 5

Explanation

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