Virus Tree 2

AtCoder

IDabc133_e

Time2000ms

Memory256MB

Difficulty—

You are given a tree with $N$ vertices and $N-1$ edges. The vertices are numbered $1$ to $N$, and the $i$\-th edge connects Vertex $a_i$ and $b_i$. You have coloring materials of $K$ colors. For each vertex in the tree, you will choose one of the $K$ colors to paint it, so that the following condition is satisfied: * If the distance between two different vertices $x$ and $y$ is less than or equal to two, $x$ and $y$ have different colors. How many ways are there to paint the tree? Find the count modulo $1\ 000\ 000\ 007$. What is tree? A tree is a kind of graph. For detail, please see: [Wikipedia "Tree (graph theory)"](https://ja.wikipedia.org/wiki/%E6%9C%A8_(%E6%95%B0%E5%AD%A6)) What is distance? The distance between two vertices $x$ and $y$ is the minimum number of edges one has to traverse to get from $x$ to $y$. ## Constraints * $1 \leq N,K \leq 10^5$ * $1 \leq a_i,b_i \leq N$ * The given graph is a tree. ## Input Input is given from Standard Input in the following format: $N$ $K$ $a_1$ $b_1$ $a_2$ $b_2$ $.$ $.$ $.$ $a_{N-1}$ $b_{N-1}$ [samples]

Samples

Input #1

Output #1

6

![image](https://img.atcoder.jp/ghi/491cd56a53e99ba7677ee4827b8f767a.png)
There are six ways to paint the tree.

Input #2

Output #2

Input #3

Output #3

271414432

API Response (JSON)

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  "problem": {
    "name": "Virus Tree 2",
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      "content": "You are given a tree with $N$ vertices and $N-1$ edges. The vertices are numbered $1$ to $N$, and the $i$\\-th edge connects Vertex $a_i$ and $b_i$. You have coloring materials of $K$ colors. For each ",
      "description_type": "Markdown"
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    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc133_e"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a tree with $N$ vertices and $N-1$ edges. The vertices are numbered $1$ to $N$, and the $i$\\-th edge connects Vertex $a_i$ and $b_i$.\nYou have coloring materials of $K$ colors. For each ...",
      "is_translate": false,
      "language": "English"
    }
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}

Full JSON Raw Segments