Simple path

AtCoder

IDabc270_c

Time2000ms

Memory256MB

Difficulty—

There is a tree $T$ with $N$ vertices. The $i$\-th edge $(1\leq i\leq N-1)$ connects vertex $U_i$ and vertex $V_i$. You are given two different vertices $X$ and $Y$ in $T$. List all vertices along the simple path from vertex $X$ to vertex $Y$ in order, including endpoints. It can be proved that, for any two different vertices $a$ and $b$ in a tree, there is a unique simple path from $a$ to $b$. What is a simple path? For vertices $X$ and $Y$ in a graph $G$, a **path** from vertex $X$ to vertex $Y$ is a sequence of vertices $v_1,v_2, \ldots, v_k$ such that $v_1=X$, $v_k=Y$, and $v_i$ and $v_{i+1}$ are connected by an edge for each $1\leq i\leq k-1$. Additionally, if all of $v_1,v_2, \ldots, v_k$ are distinct, the path is said to be a **simple path** from vertex $X$ to vertex $Y$. ## Constraints * $1\leq N\leq 2\times 10^5$ * $1\leq X,Y\leq N$ * $X\neq Y$ * $1\leq U_i,V_i\leq N$ * All values in the input are integers. * The given graph is a tree. ## Input The input is given from Standard Input in the following format: $N$ $X$ $Y$ $U_1$ $V_1$ $U_2$ $V_2$ $\vdots$ $U_{N-1}$ $V_{N-1}$ [samples]

Samples

Input #1

Output #1

2 1 3 5

The tree $T$ is shown below. The simple path from vertex $2$ to vertex $5$ is $2$ $\to$ $1$ $\to$ $3$ $\to$ $5$.  
Thus, $2,1,3,5$ should be printed in this order, with spaces in between.
![image](https://img.atcoder.jp/abc270/4f4278d90219acdbf32e838353b7a55a.png)

Input #2

Output #2

1 2

The tree $T$ is shown below.
![image](https://img.atcoder.jp/abc270/3766cc7963f74e28fa0de6ff660b1998.png)

API Response (JSON)

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  "problem": {
    "name": "Simple path",
    "description": {
      "content": "There is a tree $T$ with $N$ vertices. The $i$\\-th edge $(1\\leq i\\leq N-1)$ connects vertex $U_i$ and vertex $V_i$. You are given two different vertices $X$ and $Y$ in $T$. List all vertices along the",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc270_c"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There is a tree $T$ with $N$ vertices. The $i$\\-th edge $(1\\leq i\\leq N-1)$ connects vertex $U_i$ and vertex $V_i$.\nYou are given two different vertices $X$ and $Y$ in $T$. List all vertices along the...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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