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.Linq;
using System.IO;
using System.Text;
using static System.Math;
using static System.Array;
using static AtCoder.Tool;
namespace AtCoder
{
    class AC
    {
        const int MOD = 1000000007;
        const int INF = int.MaxValue / 2;
        const long SINF = long.MaxValue / 2;
        const double EPS = 1e-8;
        static readonly int[] dx = { 0, 1, 0, -1 };
        static readonly int[] dy = { 1, 0, -1, 0 };
        static List<List<int>> G = new List<List<int>>();
        //static List<List<Edge>>G = new List<List<Edge>>();
        //static List<Edge> E = new List<Edge>();
        static long[,] dp;
        
        static void Main(string[] args)
        {
            //var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            //Console.SetOut(sw);
            var cin = new Scanner();

            int N = int.Parse(Console.ReadLine());
            if (N == 1) { Console.WriteLine(2);return; }
            for (var i = 0; i < N; i++) G.Add(new List<int>());
            for (var i = 0; i < N - 1; i++)
            {
                var p = cin.SplitRead();
                p[0]--;p[1]--;
                G[p[0]].Add(p[1]);
                G[p[1]].Add(p[0]);
            }

            dp = new long[N, 2];

            Dfs(0, -1);
            Console.WriteLine((dp[0, 0] + dp[0, 1]) % MOD);

            //Console.Out.Flush();
        }
        static public void Dfs(int v, int parent)
        {
            dp[v, 0] = 1;dp[v, 1] = 1;

            foreach(var nv in G[v])
            {
                if (nv == parent) { continue; }
                Dfs(nv, v);
                dp[v, 0] *= (dp[nv, 0] + dp[nv, 1]);
                dp[v, 0] %= MOD;

                dp[v, 1] *= dp[nv, 0];
                dp[v, 1] %= MOD;
            }
        }
        
        struct Edge
        {
            public int from;

            public int to;
            public long dist;
            public Edge(int t, long c)
            {
                from = -1;
                to = t;
                dist = c;
            }
            public Edge(int f, int t, long c)
            {
                from = f;
                to = t;
                dist = c;
            }

        }
        struct Pair<T, U> : IComparable<Pair<T, U>>
        where T : IComparable<T>
        where U : IComparable<U>
        {
            public T first;
            public U second;
            private readonly bool CompWithFirst;

            public Pair(T f, U s, int comp)
            {
                first = f;
                second = s;
                CompWithFirst = comp == 1;
            }
            public Pair(T f, U s)
            {
                first = f;
                second = s;
                CompWithFirst = true;
            }

            public int CompareTo(Pair<T, U> other)
            {
                return CompWithFirst ? first.CompareTo(other.first) : second.CompareTo(other.second);
            }
        }
    }
    public class UnionFind
    {
        public int[] parent;
        public int[] rank;
        public int[] size;
        public UnionFind(int n)
        {
            parent = new int[n];
            rank = new int[n];
            size = new int[n];
            for (var i = 0; i < n; i++)
            {
                parent[i] = i;
                rank[i] = 0;
                size[i] = 1;
            }
        }

        private int Root(int x)
        {
            return parent[x] == x ? x : parent[x] = Root(parent[x]);
        }

        public bool SameRoot(int x, int y)
        {
            return Root(x) == Root(y);
        }

        public void Unite(int x, int y)
        {
            x = Root(x);
            y = Root(y);
            if (x == y) { return; }

            if (rank[x] < rank[y])
            {
                parent[x] = y;
                size[y] += size[x];
                size[x] = 0;
            }
            else
            {
                parent[y] = x;
                if (rank[x] == rank[y]) { rank[x]++; }
                size[x] += size[y];
                size[y] = 0;
            }
        }

        public int SizeOf(int x)
        {
            return size[Root(x)];
        }

    }
    public class PriorityQueue<T> where T : IComparable<T>
    {

        private List<T> Q;
        private readonly int r;

        public PriorityQueue(bool ascending)
        {
            if (ascending)
            {
                r = 1;
            }
            else
            {
                r = -1;
            }
            Q = new List<T>();
        }


        private void PushHeap(List<T> list, T item)
        {
            int n = list.Count();
            list.Add(item);

            while (n != 0)
            {
                int pIndex = (n - 1) / 2;

                if (list[n].CompareTo(list[pIndex]) * r > 0)
                {
                    Swap(Q, n, pIndex);
                }
                else { break; }

                n = pIndex;
            }
        }

        private void PopHeap(List<T> list)
        {
            int n = list.Count() - 1;
            list[0] = list[n];
            list.RemoveAt(n);

            int cur = 0;
            int comp;

            while (2 * cur + 1 <= n - 1)
            {
                int c1 = 2 * cur + 1;
                int c2 = 2 * (cur + 1);
                if (c1 == n - 1)
                {
                    comp = c1;
                }
                else
                {

                    comp = list[c1].CompareTo(list[c2]) * r > 0 ? c1 : c2;
                }

                if (list[cur].CompareTo(list[comp]) * r < 0)
                {
                    Swap(Q, cur, comp);
                }
                else { break; }

                cur = comp;
            }
        }

        private void Swap(List<T> list, int a, int b)
        {
            T keep = list[a];
            list[a] = list[b];
            list[b] = keep;
        }



        public void Enqueue(T value)
        {
            PushHeap(Q, value);
        }

        public T Dequeue()
        {
            T ret = Q[0];
            PopHeap(Q);
            return ret;
        }

        public T Peek()
        {
            return Q[0];
        }

        public int Count()
        {
            return Q.Count();
        }

        public bool Contains(T search)
        {
            return Q.Contains(search);
        }
    }
    public class Scanner
    {
        public int[] SplitRead()
        {
            int[] array = Console.ReadLine().Split().Select(int.Parse).ToArray();
            return array;
        }
        public long[] SplitReadL()
        {
            long[] array = Console.ReadLine().Split().Select(long.Parse).ToArray();
            return array;
        }
    }
    public static class Tool
    {
        static public void Initialize<T>(ref T[] array, T initialvalue)
        {
            for (var i = 0; i < array.Length; i++)
            {
                array[i] = initialvalue;
            }
        }
        static public void Swap<T>(T[] a, int i, int j)
        {
            T k = a[i];
            a[i] = a[j];
            a[j] = k;
        }

        static public void Display<T>(T[,] array2d, int n, int m)
        {
            for(var i = 0; i < n; i++)
            {
                for(var j = 0; j < m; j++)
                {
                    Console.Write($"{array2d[i, j]} ");
                }
                Console.WriteLine();
            }
        }

    }

}