The directed graph is given. Find the shortest distance from the vertex x to other vertices of the graph.
The first line contains two integers n and x (1≤n≤1000,1≤x≤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.
Print the numbers d1,d2,...,dn, where di is −1 if there is no path from x to i, or the minimal distance from x to i otherwise.