Orientation

AtCoder

IDarc111_d

Time2000ms

Memory256MB

Difficulty—

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: $c_1, c_2, \cdots, c_N$. Convert 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 $b_i \to a_i$. * 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. In this problem, it is guaranteed that the given input **always has a solution**. ## Constraints * $1 \leq N \leq 100$ * $0 \leq M \leq \frac{N(N - 1)}{2}$ * $1 \leq a_i, b_i \leq N$ * The given graph has no self-loops and no multi-edges. * $1 \leq c_i \leq N$ * **There always exists a valid solution.** ## Input Input is given from Standard Input in the following format: $N$ $M$ $a_1$ $b_1$ $:$ $a_M$ $b_M$ $c_1$ $c_2$ $...$ $c_N$ [samples]

Samples

Input #1

Output #1

\->
->
->

In a cycle of length $3$, you can reach every vertex from any vertex.

Input #2

Output #2

<-
<-

Input #3

6 3
1 2
4 3
5 6
1 2 1 2 2 1

Output #3

<-
->
->

The graph may be disconnected.

API Response (JSON)

{
  "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 positi...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments