Good Vertices

AtCoder

IDabc236_g

Time2000ms

Memory256MB

Difficulty—

We have a directed graph with $N$ vertices. The $N$ vertices are called Vertex $1$, Vertex $2$, $\ldots$, Vertex $N$. At time $0$, the graph has no edge. For each $t = 1, 2, \ldots, T$, at time $t$, a directed edge from Vertex $u_t$ to Vertex $v_t$ will be added. (The edge may be a self-loop, that is, $u_t = v_t$ may hold.) A vertex is called _good_ when it can be reached by starting at Vertex $1$ and traversing an edge **exactly** $L$ times. For each $i = 1, 2, \ldots, N$, print the earliest time when Vertex $i$ is good. If there is no time when Vertex $i$ is good, print $-1$ instead. ## Constraints * $2 \leq N \leq 100$ * $1 \leq T \leq N^2$ * $1 \leq L \leq 10^9$ * $1 \leq u_t, v_t \leq N$ * $i \neq j \Rightarrow (u_i, v_i) \neq (u_j, v_j)$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $T$ $L$ $u_1$ $v_1$ $u_2$ $v_2$ $\vdots$ $u_T$ $v_T$ [samples]

Samples

Input #1

Output #1

\-1 4 5 3

At time $0$, the graph has no edge. Afterward, edges are added as follows.

*   At time $1$, a directed edge from Vertex $2$ to Vertex $3$ is added.
*   At time $2$, a directed edge from Vertex $3$ to Vertex $4$ is added.
*   At time $3$, a directed edge from Vertex $1$ to Vertex $2$ is added. Now, Vertex $4$ can be reached from Vertex $1$ in exactly three moves: $1 \rightarrow 2 \rightarrow 3 \rightarrow 4$, making Vertex $4$ good.
*   At time $4$, a directed edge from Vertex $3$ to Vertex $2$ is added. Now, Vertex $2$ can be reached from Vertex $1$ in exactly three moves: $1 \rightarrow 2 \rightarrow 3 \rightarrow 2$, making Vertex $2$ good.
*   At time $5$, a directed edge (self-loop) from Vertex $2$ to Vertex $2$ is added. Now, Vertex $3$ can be reached from Vertex $1$ in exactly three moves: $1 \rightarrow 2 \rightarrow 2 \rightarrow 3$, making Vertex $3$ good.

Vertex $1$ will never be good.

Input #2

2 1 1000000000
1 2

Output #2

\-1 -1

API Response (JSON)

{
  "problem": {
    "name": "Good Vertices",
    "description": {
      "content": "We have a directed graph with $N$ vertices. The $N$ vertices are called Vertex $1$, Vertex $2$, $\\ldots$, Vertex $N$. At time $0$, the graph has no edge. For each $t = 1, 2, \\ldots, T$, at time $t$, a",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc236_g"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have a directed graph with $N$ vertices. The $N$ vertices are called Vertex $1$, Vertex $2$, $\\ldots$, Vertex $N$. At time $0$, the graph has no edge.\nFor each $t = 1, 2, \\ldots, T$, at time $t$, a...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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