Bridges

Find bridges of an undirected graph G(V, E).

A bridge (also known as a cut-edge) is an edge whose deletion increase the number of connected components.

Constraints

• 1 ≤ |V| ≤ 100,000
• 0 ≤ |E| ≤ 100,000
• The graph is connected
• There are no parallel edges
• There are no self-loops

Input

|V| |E| s0 t0 s1 t1 : s|E|-1 t|E|-1

, where |V| is the number of nodes and |E| is the number of edges in the graph. The graph nodes are named with the numbers 0, 1,..., |V|-1 respectively.

si and ti represent source and target nodes of i-th edge (undirected).

Output

A list of bridges of the graph ordered by name. For each bridge, names of its end-ponints, source and target (source < target), should be printed separated by a space. The sources should be printed ascending order, then the target should also be printed ascending order for the same source.

Examples

Input

4 4 0 1 0 2 1 2 2 3

Output

2 3

Input

5 4 0 1 1 2 2 3 3 4

Output

0 1 1 2 2 3 3 4

inputFormat

Input

|V| |E| s0 t0 s1 t1 : s|E|-1 t|E|-1

, where |V| is the number of nodes and |E| is the number of edges in the graph. The graph nodes are named with the numbers 0, 1,..., |V|-1 respectively.

si and ti represent source and target nodes of i-th edge (undirected).

outputFormat

Output

A list of bridges of the graph ordered by name. For each bridge, names of its end-ponints, source and target (source < target), should be printed separated by a space. The sources should be printed ascending order, then the target should also be printed ascending order for the same source.

Examples

Input

4 4 0 1 0 2 1 2 2 3

Output

2 3

Input

5 4 0 1 1 2 2 3 3 4

Output

0 1 1 2 2 3 3 4

样例

5 4
0 1
1 2
2 3
3 4

0 1
1 2
2 3
3 4

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