Problem:
Score : 100 points

Problem Statement

There is a tree with N vertices, numbered 1, 2, \ldots, N.
For each i (1 \leq i \leq N - 1), the i-th edge connects Vertex x_i and y_i.

Taro has decided to paint each vertex in white or black.
Here, it is not allowed to paint two adjacent vertices both in black.

Find the number of ways in which the vertices can be painted, modulo 10^9 + 7.

Constraints

All values in input are integers.

1 \leq N \leq 10^5

1 \leq x_i, y_i \leq N

The given graph is a tree.

Input

Input is given from Standard Input in the following format:

N
x_1 y_1
x_2 y_2
:
x_{N - 1} y_{N - 1}

Output

Print the number of ways in which the vertices can be painted, modulo 10^9 + 7.

Sample Input 1

3
1 2
2 3

Sample Output 1

5

There are five ways to paint the vertices, as follows:

Sample Input 2

4
1 2
1 3
1 4

Sample Output 2

9

There are nine ways to paint the vertices, as follows:

Sample Input 3

1

Sample Output 3

2

Sample Input 4

10
8 5
10 8
6 5
1 5
4 8
2 10
3 6
9 2
1 7

Sample Output 4

157

Solution in C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Linq;//リストの使用
using System.Collections.Generic;
using System.Text;//テキストの高速出力に必要
class Program
{
static int n = int.Parse(Console.ReadLine());
static long mod = 1000000007;
static List<int>[] nextList = new List<int>[n];//隣接リスト（リストの入った配列）
static long[,] dp = new long[n,2];

	static void Main()
	{
    for(int i = 0; i < n; i++)
    {
      nextList[i] = new List<int>();//リストの宣言
      dp[i,0] = -1;
      dp[i,1] = -1;
    }
    for(int i = 0; i < n-1; i++)
    {
      int[] nums = Array.ConvertAll(Console.ReadLine().Split(' '),int.Parse);
      nextList[nums[0]-1].Add(nums[1]-1);//隣接リストへ追加。
      nextList[nums[1]-1].Add(nums[0]-1);
    }
    
		Console.WriteLine(DP(0,0)+DP(0,1));
	}

  static long DP(int vertexNum, int colorNum)
  {
    if(dp[vertexNum,colorNum] != -1) return dp[vertexNum,colorNum];
    
    dp[vertexNum,colorNum] = 1;
    
    if(colorNum == 0)
    {
      for(int i = 0; i < nextList[vertexNum].Count; i++)
      {
        int partnerNum = nextList[vertexNum][i];
        nextList[partnerNum].Remove(vertexNum);//木の逆走を防ぐ
        dp[vertexNum,colorNum] *= (DP(partnerNum,0) + DP(partnerNum,1))%mod;
        //dp[vertexNum,colorNum] %= mod;
      }
      //Console.WriteLine(vertexNum+" "+colorNum+" "+dp[vertexNum,colorNum]);
      return dp[vertexNum,colorNum];
    }else
    {
      for(int i = 0; i < nextList[vertexNum].Count; i++)
      {
        int partnerNum = nextList[vertexNum][i];
        nextList[partnerNum].Remove(vertexNum);
        dp[vertexNum,colorNum] *= DP(partnerNum,0);
        //dp[vertexNum,colorNum] %= mod;
      }
      //Console.WriteLine(vertexNum+" "+colorNum+" "+dp[vertexNum,colorNum]);
      return dp[vertexNum,colorNum];
    }

    return 0;
  }
}