{"raw_statement":[{"iden":"problem statement","content":"You are given a simple connected undirected graph with $N$ vertices and $M$ edges. The vertices are numbered $1$ to $N$, and the $i$\\-th edge connects Vertex $A_i$ and Vertex $B_i$. Takahashi will assign one of the two possible directions to each of the edges in the graph to make a directed graph. Determine if it is possible to make a directed graph with an even number of edges going out from every vertex. If the answer is yes, construct one such graph."},{"iden":"notes","content":"An undirected graph is said to be simple when it contains no self-loops or multiple edges."},{"iden":"constraints","content":"*   $2 \\leq N \\leq 10^5$\n*   $N-1 \\leq M \\leq 10^5$\n*   $1 \\leq A_i,B_i \\leq N (1\\leq i\\leq M)$\n*   The given graph is simple and connected."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $M$\n$A_1$ $B_1$\n$:$\n$A_M$ $B_M$"},{"iden":"sample input 1","content":"4 4\n1 2\n2 3\n3 4\n4 1"},{"iden":"sample output 1","content":"1 2\n1 4\n3 2\n3 4\n\nAfter this assignment of directions, Vertex $1$ and $3$ will each have two outgoing edges, and Vertex $2$ and $4$ will each have zero outgoing edges."},{"iden":"sample input 2","content":"5 5\n1 2\n2 3\n3 4\n2 5\n4 5"},{"iden":"sample output 2","content":"\\-1"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}