# [Solution] Tree Coloring solution codechef

## Tree Coloring solution codechef

Tree Coloring solution codechef – Given a tree containing N nodes.

Each node can be coloured using exactly one of the C colours. Find the number of colourings of the tree such that:

• All nodes in a path of length at most two have distinct colours.

As the answer can be huge, print it modulo (10 ^ 9 + 7).

Note:

• Two colourings of a tree are different if there exists at least one node having different colours in both the colourings.
• A path in a tree is a sequence of (zero or more) connected nodes.
• The path length between two nodes is defined as the total number of edges in the shortest path from one node to other.

## Tree Coloring solution codechef

• The first line of the input will contain two integers N and C, the number of nodes in the tree and the number of colours available respectively.
• The next (N – 1) lines will describe the given tree. Each line contains two integers U and V meaning that there is an edge between node U and node V.

### Output Format

• Output the number of ways to colour the tree satisfying the given condition, modulo 10^9 + 7.

### Constraints

• 1 \leq N \leq 10^6
• 1 \leq C \leq 10^6
• 1 \leq U, V \leq N

## Tree Coloring solution codechef

Input

Output

3 3
1 2
1 3

6


## Tree Coloring solution codechef

The valid colourings of nodes 1, 2, and 3 are: \{1, 2, 3\}, \{1, 3, 2\}, \{2, 1, 3\}, \{2, 3, 1\}, \{3, 1, 2\}, and \{3, 2, 1\}.