{"problem":{"name":"Even Degrees","description":{"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 ass","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"agc035_b"},"statements":[{"statement_type":"Markdown","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.\n\n## Constraints\n\n*   $2 \\leq N \\leq 10^5$\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.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$ $M$\n$A_1$ $B_1$\n$:$\n$A_M$ $B_M$\n\n[samples]\n\n## Notes\n\nAn undirected graph is said to be simple when it contains no self-loops or multiple edges.","is_translate":false,"language":"English"}],"meta":{"iden":"agc035_b","tags":[],"sample_group":[["4 4\n1 2\n2 3\n3 4\n4 1","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."],["5 5\n1 2\n2 3\n3 4\n2 5\n4 5","\\-1"]],"created_at":"2026-03-03 11:01:14"}}