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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;

#define ll  long long
#define PII pair<ll,ll>
#define VI  vector<ll>
#define VB  vector<bool>
#define VC vector<char>
#define VVI vector<vector<ll>>
#define VVC vector<vector<char>>
#define VS  vector<string>
#define VP  vector<PII>
#define lf(i,a,b) for(ll i=a;i<=b;i++)
#define lr(i,a,b) for(ll i=a;i>=b;i--)
#define lfl(i,v) for(ll i=0;i<v.size();i++)
#define lrl(i,v) for(ll i=(ll)(v.size())-1;i>=0;i--)
#define chk2(a,b) cout<<"check :  "<<a<<" "<<b<<endl
#define chk3(a,b,c) cout<<"check :  "<<a<<" "<<b<<" "<<c<<endl
#define chk4(a,b,c,d) cout<<"check :  "<<a<<" "<<b<<" "<<c<<" "<<d<<endl
#define chk5(a,b,c,d,e) cout<<"check :  "<<a<<" "<<b<<" "<<c<<" "<<d<<" "<<e<<endl
#define l_b(v,k)  lower_bound(v.begin(),v.end(),k)-v.begin()
#define u_b(v,k)  upper_bound(v.begin(),v.end(),k)-v.begin()
#define mod 1000000007
#define sort(v) sort(v.begin(),v.end())
#define p_b push_back
#define p_f push_front
#define m_p make_pair
#define fir first
#define sec second
#define sz size()
ll n,m,k;
VVI tr;
ll dp[100005][2];
ll fun(ll v,ll par,ll cl)
    {   if(dp[v][cl]!=-1)
            return dp[v][cl];
        ll mul=1;
        if(cl==0)
        {   lfl(i,tr[v])
            {   if(par!=tr[v][i])
                {   ll sum=(fun(tr[v][i],v,0)+fun(tr[v][i],v,1))%mod;
                    mul=(mul*sum)%mod;
                }
            }
        }
        else
        {   lfl(i,tr[v])
            {   if(par!=tr[v][i])
                {   ll sum=(fun(tr[v][i],v,0))%mod;
                    mul=(mul*sum)%mod;
                }
            }
        }
        return dp[v][cl]=mul;
    }
int main() 
{   cin>>n;
    tr=VVI(n+1);
    lf(i,1,n-1)
    {   ll u,v;cin>>u>>v;
        tr[u].p_b(v);
        tr[v].p_b(u);
    }
    memset(dp,-1,sizeof(dp));
    cout<<(fun(1,-1,0)+fun(1,-1,1))%mod<<endl;
}