{"problem":{"name":"Orientation","description":{"content":"Given is a simple undirected graph with $N$ vertices and $M$ edges. The vertices are numbered $1, \\cdots, N$, and the $i$\\-th edge connects Vertices $a_i$ and $b_i$. Also given is a sequence of positi","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"arc111_d"},"statements":[{"statement_type":"Markdown","content":"Given is a simple undirected graph with $N$ vertices and $M$ edges. The vertices are numbered $1, \\cdots, N$, and the $i$\\-th edge connects Vertices $a_i$ and $b_i$. Also given is a sequence of positive integers: $c_1, c_2, \\cdots, c_N$.\nConvert this graph into a directed graph that satisfies the condition below, that is, for each $i$, delete the undirected edge $(a_i, b_i)$ and add one of the two direted edges $a_i \\to b_i$ and $b_i \\to a_i$.\n\n*   For every $i = 1, 2, \\cdots, N$, there are exactly $c_i$ vertices reachable from Vertex $i$ (by traversing some number of directed edges), including Vertex $i$ itself.\n\nIn this problem, it is guaranteed that the given input **always has a solution**.\n\n## Constraints\n\n*   $1 \\leq N \\leq 100$\n*   $0 \\leq M \\leq \\frac{N(N - 1)}{2}$\n*   $1 \\leq a_i, b_i \\leq N$\n*   The given graph has no self-loops and no multi-edges.\n*   $1 \\leq c_i \\leq N$\n*   **There always exists a valid solution.**\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$c_1$ $c_2$ $...$ $c_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"arc111_d","tags":[],"sample_group":[["3 3\n1 2\n2 3\n3 1\n3 3 3","\\->\n->\n->\n\nIn a cycle of length $3$, you can reach every vertex from any vertex."],["3 2\n1 2\n2 3\n1 2 3","<-\n<-"],["6 3\n1 2\n4 3\n5 6\n1 2 1 2 2 1","<-\n->\n->\n\nThe graph may be disconnected."]],"created_at":"2026-03-03 11:01:14"}}