The connected undirected graph without loops and multiple edges is given. You are allowed to remove the edges from it. Obtain a tree from the graph.

Input

The first line contains the number of vertices n (1 ≤ n ≤ 100) and the number of edges m of the graph. The next m pairs of numbers define the edges. It is guaranteed that the graph is connected.

Output

Print n - 1 pairs of numbers - the edges that will be included in a tree. The edges can be displayed in any order.