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 PyPy3 (2.4.0) (judge verdict: Accepted)

import sys
def input(): return sys.stdin.readline().rstrip()
from collections import deque
def main():
    n=int(input())
    XY=[tuple(map(int,input().split())) for i in range(n-1)]
    graph=[[]for _ in range(n)]
    for x,y in XY:
        graph[x-1].append(y-1)
        graph[y-1].append(x-1)
    queue=deque([0])
    visited=[False]*n
    use=[False]*n
    #i番目に訪れた頂点までについて，i番目の頂点を白に塗る塗り方，黒
    dp=[[0,0] for _ in range(n)]
    mod=10**9+7
    while queue:
        node=queue[-1] #末尾の要素がvisited→葉に着いた
        if not visited[node]:
            visited[node]=True
            for xnode in graph[node]:
                if visited[xnode]:continue
                queue.append(xnode)
        else:
            queue.pop()
            b,w=1,1
            for xnode in graph[node]:   
                if use[xnode]:
                    w=w*(dp[xnode][0]+dp[xnode][1])%mod
                    b=b*dp[xnode][0]%mod 
            dp[node][0]=w%mod
            dp[node][1]=b%mod 
            use[node]=True
    print(sum(dp[0])%mod)

if __name__=='__main__':
    main()