Competitions

# Breadth First Search

# The shortest distance

The directed graph is given. Find the shortest distance from the vertex **x** to other vertices of the graph.

#### Input

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. 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.

#### Output

Print the numbers `d`

, _{1}`d`

, ..., _{2}`d`

, separated with a space, where _{n}`d`

is _{i}**-1** if there is no path from **x** to **i**, or the minimal distance from **x** to **i** otherwise.

Input example #1

6 5 0 1 1 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 0

Output example #1

2 2 1 1 0 -1