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: Accepted)

using System;
using System.Collections.Generic;
using System.Text;

namespace AtTest.EducationalDP
{
    class P
    {
        static long mask = 1000000000 + 7;

        static void Main(string[] args)
        {
            Method(args);
            Console.ReadLine();
        }

        static void Method(string[] args)
        {
            int n = ReadInt();
            List<int>[] graph = new List<int>[n];
            for (int i = 0; i < n; i++) graph[i] = new List<int>();
            for(int i = 0; i < n - 1; i++)
            {
                int[] xy = ReadInts();
                int x = xy[0] - 1;
                int y = xy[1] - 1;
                graph[x].Add(y);
                graph[y].Add(x);
            }
            long[,] dp = new long[n, 2];//j=0:white,j=1:black
            bool[] visit = new bool[n];
            DFS(ref dp,ref visit, graph, 0);
            Console.WriteLine((dp[0, 0] + dp[0, 1]) % mask);
        }

        static void DFS(ref long[,] dp,ref bool[] visit,
            List<int>[] graph, int now)
        {
            visit[now] = true;
            
            dp[now, 0] = 1;
            dp[now, 1] = 1;
            for (int i = 0; i < graph[now].Count; i++)
            {
                int to = graph[now][i];
                if (visit[to]) continue;

                DFS(ref dp,ref visit, graph, to);
                dp[now, 0] *= (dp[to, 0] + dp[to, 1]) % mask;
                dp[now, 0] %= mask;
                dp[now, 1] *= dp[to, 0];
                dp[now, 1] %= mask;
            }
        }

        private static string Read() { return Console.ReadLine(); }
        private static int ReadInt() { return int.Parse(Read()); }
        private static long ReadLong() { return long.Parse(Read()); }
        private static double ReadDouble() { return double.Parse(Read()); }
        private static int[] ReadInts() { return Array.ConvertAll(Read().Split(), int.Parse); }
        private static long[] ReadLongs() { return Array.ConvertAll(Read().Split(), long.Parse); }
        private static double[] ReadDoubles() { return Array.ConvertAll(Read().Split(), double.Parse); }
    }
}