The directed graph is given. Find the shortest distance from the vertex $x$ to other vertices of the graph. \InputFile The first line contains two integers $n$ and $x~(1 \le n \le 1000, 1 \le x \le n)$ --- the number of vertices in a graph and the starting vertex. Each of the next $n$ lines contains $n$ numbers --- the adjacency matrix of the graph: the $i$-th line and $j$-th column contains "$1$", if the vertices $i$ and $j$ are connected with the edge, and "$0$", if there is no edge between them. The main diagonal contains zeroes. \OutputFile Print the numbers $d_1, d_2, ..., d_n$, where $d_i$ is $-1$ if there is no path from $x$ to $i$, or the minimal distance from $x$ to $i$ otherwise. \includegraphics{https://static.e-olymp.com/content/c2/c224136cf9f3a3d3b7373c352ad4f8cb1c436ddd.gif}