Return to 1

AtCoder

IDabc306_g

Time2000ms

Memory256MB

Difficulty—

We have a directed graph with $N$ vertices and $M$ edges. The vertices are numbered from $1$ through $N$, and the $i$\-th edge goes from vertex $U_i$ to vertex $V_i$. You are currently at vertex $1$. Determine if you can make the following move $10^{10^{100}}$ times to end up at vertex $1$: * choose an edge going from the vertex you are currently at, and move to the vertex that the edge points at. Given $T$ test cases, solve each of them. ## Constraints * All input values are integers. * $1\leq T \leq 2\times 10^5$ * $2\leq N \leq 2\times 10^5$ * $1\leq M \leq 2\times 10^5$ * The sum of $N$ over all test cases is at most $2 \times 10^5$. * The sum of $M$ over all test cases is at most $2 \times 10^5$. * $1 \leq U_i, V_i \leq N$ * $U_i \neq V_i$ * If $i\neq j$, then $(U_i,V_i) \neq (U_j,V_j)$. ## Input The input is given from Standard Input in the following format. Here, $\text{test}_i$ denotes the $i$\-th test case. $T$ $\text{test}_1$ $\text{test}_2$ $\vdots$ $\text{test}_T$ Each test case is given in the following format. $N$ $M$ $U_1$ $V_1$ $U_2$ $V_2$ $\vdots$ $U_M$ $V_M$ [samples]

Samples

Input #1

Output #1

Yes
No
No
Yes

For the $1$\-st test case,

*   You inevitably repeat visiting vertices $1 \rightarrow 2 \rightarrow 1 \rightarrow \dots$. Thus, you will end up at vertex $1$ after making the move $10^{10^{100}}$ times, so the answer is `Yes`.

For the $2$\-nd test case,

*   You inevitably repeat visiting vertices $1 \rightarrow 2 \rightarrow 3 \rightarrow 1 \rightarrow \dots$. Thus, you will end up at vertex $2$ after making the move $10^{10^{100}}$ times, so the answer is `No`.

API Response (JSON)

{
  "problem": {
    "name": "Return to 1",
    "description": {
      "content": "We have a directed graph with $N$ vertices and $M$ edges. The vertices are numbered from $1$ through $N$, and the $i$\\-th edge goes from vertex $U_i$ to vertex $V_i$. You are currently at vertex $1$. ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc306_g"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have a directed graph with $N$ vertices and $M$ edges. The vertices are numbered from $1$ through $N$, and the $i$\\-th edge goes from vertex $U_i$ to vertex $V_i$.\nYou are currently at vertex $1$. ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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