Subtree K-th Max

AtCoder

IDabc239_e

Time2000ms

Memory256MB

Difficulty—

We have a rooted tree with $N$ vertices. The vertices are numbered $1$ through $N$, and the root is Vertex $1$. The $i$\-th edge connects Vertices $A_i$ and $B_i$. Vertex $i$ has an integer $X_i$ written on it. You are given $Q$ queries. For the $i$\-th query, given a pair of integers $(V_i,K_i)$, answer the following question. * Question: among the integers written on the vertices in the subtree rooted at Vertex $V_i$, find the $K_i$\-th largest value. ## Constraints * $2 \leq N \leq 10^5$ * $0\leq X_i\leq 10^9$ * $1\leq A_i,B_i\leq N$ * $1\leq Q \leq 10^5$ * $1\leq V_i\leq N$ * $1\leq K_i\leq 20$ * The given graph is a tree. * The subtree rooted at Vertex $V_i$ has $K_i$ or more vertices. * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $Q$ $X_1$ $\ldots$ $X_N$ $A_1$ $B_1$ $\vdots$ $A_{N-1}$ $B_{N-1}$ $V_1$ $K_1$ $\vdots$ $V_Q$ $K_Q$ [samples]

Samples

Input #1

Output #1

4
5

The tree given in this input is shown below.
![image](https://img.atcoder.jp/ghi/e2bc1237d64f79f33181e6f54c9f7ce7.png)
For the $1$\-st query, the vertices in the subtree rooted at Vertex $1$ are Vertices $1, 2, 3, 4$, and $5$, so print the $2$\-nd largest value of the numbers written on these vertices, $4$.  
For the $2$\-nd query, the vertices in the subtree rooted at Vertex $2$ are Vertices $2, 3$, and $5$, so print the $1$\-st largest value of the numbers written on these vertices, $5$.

Input #2

6 2
10 10 10 9 8 8
1 4
2 1
2 5
3 2
6 4
1 4
2 2

Output #2

9
10

Input #3

4 4
1 10 100 1000
1 2
2 3
3 4
1 4
2 3
3 2
4 1

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Subtree K-th Max",
    "description": {
      "content": "We have a rooted tree with $N$ vertices. The vertices are numbered $1$ through $N$, and the root is Vertex $1$.   The $i$\\-th edge connects Vertices $A_i$ and $B_i$.   Vertex $i$ has an integer $X_i$ ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc239_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have a rooted tree with $N$ vertices. The vertices are numbered $1$ through $N$, and the root is Vertex $1$.  \nThe $i$\\-th edge connects Vertices $A_i$ and $B_i$.  \nVertex $i$ has an integer $X_i$ ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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