Colorful Tree

AtCoder

IDabc133_f

Time4000ms

Memory256MB

Difficulty—

There is a tree with $N$ vertices numbered $1$ to $N$. The $i$\-th edge in this tree connects Vertex $a_i$ and Vertex $b_i$, and the color and length of that edge are $c_i$ and $d_i$, respectively. Here the color of each edge is represented by an integer between $1$ and $N-1$ (inclusive). The same integer corresponds to the same color, and different integers correspond to different colors. Answer the following $Q$ queries: * Query $j$ ($1 \leq j \leq Q$): assuming that the length of every edge whose color is $x_j$ is changed to $y_j$, find the distance between Vertex $u_j$ and Vertex $v_j$. (The changes of the lengths of edges do not affect the subsequent queries.) ## Constraints * $2 \leq N \leq 10^5$ * $1 \leq Q \leq 10^5$ * $1 \leq a_i, b_i \leq N$ * $1 \leq c_i \leq N-1$ * $1 \leq d_i \leq 10^4$ * $1 \leq x_j \leq N-1$ * $1 \leq y_j \leq 10^4$ * $1 \leq u_j < v_j \leq N$ * The given graph is a tree. * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $Q$ $a_1$ $b_1$ $c_1$ $d_1$ $:$ $a_{N-1}$ $b_{N-1}$ $c_{N-1}$ $d_{N-1}$ $x_1$ $y_1$ $u_1$ $v_1$ $:$ $x_Q$ $y_Q$ $u_Q$ $v_Q$ [samples]

Samples

Input #1

Output #1

130
200
60

The graph in this input is as follows:
![image](https://img.atcoder.jp/ghi/ca75688b08f73eb63a30ce6daa54a781.png)
Here the edges of Color $1$ are shown as solid red lines, the edge of Color $2$ is shown as a bold green line, and the edge of Color $4$ is shown as a blue dashed line.

*   Query $1$: Assuming that the length of every edge whose color is $1$ is changed to $100$, the distance between Vertex $1$ and Vertex $4$ is $100 + 30 = 130$.
*   Query $2$: Assuming that the length of every edge whose color is $1$ is changed to $100$, the distance between Vertex $1$ and Vertex $5$ is $100 + 100 = 200$.
*   Query $3$: Assuming that the length of every edge whose color is $3$ is changed to $1000$ (there is no such edge), the distance between Vertex $3$ and Vertex $4$ is $20 + 10 + 30 = 60$. Note that the edges of Color $1$ now have their original lengths.

API Response (JSON)

{
  "problem": {
    "name": "Colorful Tree",
    "description": {
      "content": "There is a tree with $N$ vertices numbered $1$ to $N$. The $i$\\-th edge in this tree connects Vertex $a_i$ and Vertex $b_i$, and the color and length of that edge are $c_i$ and $d_i$, respectively. He",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 4000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc133_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There is a tree with $N$ vertices numbered $1$ to $N$. The $i$\\-th edge in this tree connects Vertex $a_i$ and Vertex $b_i$, and the color and length of that edge are $c_i$ and $d_i$, respectively. He...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments