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.Diagnostics;
using System.Globalization;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Text;
using System.Text.RegularExpressions;
using System.Threading;

namespace ReadWriteTemplate
{
    public static class Solver
    {
        private static void SolveCase()
        {
            int n = ReadInt();
            var v = new Vertex[n];
            for (int i = 0; i < n; i++)
            {
                v[i] = new Vertex();
            }
            for (int i = 0; i < n - 1; i++)
            {
                int x = ReadInt() - 1;
                int y = ReadInt() - 1;
                v[x].Edges.Add(v[y]);
                v[y].Edges.Add(v[x]);
            }

            v[0].Dfs();

            long ans = v[0].Total % Vertex.MOD;

            Writer.WriteLine(ans);
        }

        public class Vertex
        {
            public const long MOD = 1000000007;

            public List<Vertex> Edges = new List<Vertex>();

            public long White;

            public long Black;

            public long Total => White + Black;

            public bool Used;

            public void Dfs()
            {
                Used = true;

                White = 1;
                Black = 1;

                foreach (Vertex vertex in Edges)
                {
                    if (!vertex.Used)
                    {
                        vertex.Dfs();

                        Black = Black * vertex.White % MOD;
                        White = White * vertex.Total % MOD;
                    }
                }
            }
        }

        public static void Solve()
        {
#if DEBUG
            var sw = Stopwatch.StartNew();
#endif

            SolveCase();

            /*int T = ReadInt();
            for (int i = 0; i < T; i++)
            {
                // Writer.WriteLine("Case {0}:", i + 1);
                // Writer.Write("Case #{0}: ", i + 1);
                SolveCase();
            }*/

#if DEBUG
            sw.Stop();
            Console.WriteLine($"{sw.ElapsedMilliseconds} ms");
#endif
        }

        public static void Main()
        {
            Thread.CurrentThread.CurrentCulture = CultureInfo.InvariantCulture;

#if DEBUG
            // Reader = Console.In; Writer = Console.Out;
            Reader = File.OpenText("input.txt"); Writer = File.CreateText("output.txt");
#else
            Reader = Console.In; Writer = Console.Out;
#endif

            // Solve();
            Thread thread = new Thread(Solve, 64 * 1024 * 1024);
            thread.CurrentCulture = CultureInfo.InvariantCulture;
            thread.Start();
            thread.Join();

            Reader.Close();
            Writer.Close();
        }

        public static IOrderedEnumerable<TSource> OrderByWithShuffle<TSource, TKey>(this IEnumerable<TSource> source, Func<TSource, TKey> keySelector)
        {
            return source.Shuffle().OrderBy(keySelector);
        }

        public static T[] Shuffle<T>(this IEnumerable<T> source)
        {
            T[] result = source.ToArray();
            Random rnd = new Random();
            for (int i = result.Length - 1; i >= 1; i--)
            {
                int k = rnd.Next(i + 1);
                T tmp = result[k];
                result[k] = result[i];
                result[i] = tmp;
            }
            return result;
        }

        #region Read/Write

        private static TextReader Reader;

        private static TextWriter Writer;

        private static Queue<string> CurrentLineTokens = new Queue<string>();

        private static string[] ReadAndSplitLine()
        {
            return Reader.ReadLine().Split(new[] { ' ', '\t' }, StringSplitOptions.RemoveEmptyEntries);
        }

        public static string ReadToken()
        {
            while (CurrentLineTokens.Count == 0)
                CurrentLineTokens = new Queue<string>(ReadAndSplitLine());
            return CurrentLineTokens.Dequeue();
        }

        public static string ReadLine()
        {
            return Reader.ReadLine();
        }

        public static int ReadInt()
        {
            return int.Parse(ReadToken());
        }

        public static long ReadLong()
        {
            return long.Parse(ReadToken());
        }

        public static double ReadDouble()
        {
            return double.Parse(ReadToken(), CultureInfo.InvariantCulture);
        }

        public static int[] ReadIntArray()
        {
            return ReadAndSplitLine().Select(int.Parse).ToArray();
        }

        public static long[] ReadLongArray()
        {
            return ReadAndSplitLine().Select(long.Parse).ToArray();
        }

        public static double[] ReadDoubleArray()
        {
            return ReadAndSplitLine().Select(s => double.Parse(s, CultureInfo.InvariantCulture)).ToArray();
        }

        public static int[][] ReadIntMatrix(int numberOfRows)
        {
            int[][] matrix = new int[numberOfRows][];
            for (int i = 0; i < numberOfRows; i++)
                matrix[i] = ReadIntArray();
            return matrix;
        }

        public static string[] ReadLines(int quantity)
        {
            string[] lines = new string[quantity];
            for (int i = 0; i < quantity; i++)
                lines[i] = Reader.ReadLine().Trim();
            return lines;
        }

        public static void WriteArray<T>(IEnumerable<T> array)
        {
            Writer.WriteLine(string.Join(" ", array));
        }

        #endregion
    }
}