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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.*;
import java.lang.*;
import java.io.*;

class Main
{
	static long MOD = 1000000007;
	static Long dp[][];

	static long getWays(ArrayList<Integer> tree[], int curr, int par, int color)
	{
		if(tree[curr].size()==1 && tree[curr].get(0)==par)
		{
			return 1;
		}

		if(dp[curr][color]!=null)
			return dp[curr][color];

		long temp=1;

		if(color==1)
		{
			for(int ch: tree[curr])
			{
				if(ch==par)
					continue;
				temp *= getWays(tree, ch, curr, 0);
				temp = temp%MOD;
			}
		}
		else
		{
			for(int ch: tree[curr])
			{
				if(ch==par)
					continue;
				temp *= (getWays(tree, ch, curr, 0)%MOD + getWays(tree, ch, curr, 1)%MOD);
				temp = temp%MOD;
			}
		}
		return dp[curr][color]=temp;
	}

	public static void main(String[] args)
	{
		FastReader scan=new FastReader();
		int n=scan.nextInt();
		ArrayList<Integer> tree[]=new ArrayList[n];
		for(int i=0;i<n;i++)
			tree[i]=new ArrayList<>();

		for(int i=0;i<n-1;i++)
		{
			int u=scan.nextInt()-1;
			int v=scan.nextInt()-1;

			tree[u].add(v);
			tree[v].add(u);
		}

		dp=new Long[n][2];
		long ans = getWays(tree, 0, -1, 0)%MOD + getWays(tree, 0, -1, 1)%MOD;
		ans = ans%MOD;

		System.out.println(ans);

	}


static class FastReader
{
    BufferedReader br;
    StringTokenizer st;
 
    public FastReader()
    {
        br = new BufferedReader(new
                InputStreamReader(System.in));
    }
 
    String next()
    {
        while (st == null || !st.hasMoreElements())
        {
            try
            {
                st = new StringTokenizer(br.readLine());
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
        }
        return st.nextToken();
    }
 
    int nextInt()
    {
        return Integer.parseInt(next());
    }
 
    long nextLong()
    {
        return Long.parseLong(next());
    }
 
    double nextDouble()
    {
        return Double.parseDouble(next());
    }
 
    String nextLine()
    {
        String str = "";
        try
        {
            str = br.readLine();
        }
        catch (IOException e)
        {
            e.printStackTrace();
        }
        return str;
    }
}



}