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 Rust (1.42.0) (judge verdict: Accepted)

#![allow(unused_macros)]
#![allow(dead_code)]
#![allow(unused_imports)]

use text_io::*;

fn main() {
    const U_INF: usize = 1 << 60;
    const I_INF: isize = 1 << 60;

    //ただの頂点の受け取り。O(2(n-1))
    let n: usize = read!();
    let mut vertexes = vec![vec![]; n];
    for _ in 1..n {
        let mut xi: usize = read!();
        let mut yi: usize = read!();
        xi -= 1;
        yi -= 1;
        vertexes[xi].push(yi);
        vertexes[yi].push(xi);
    }

    let mut dp = vec![vec![None; 2]; n + 10];

    //頂点0に対して色が白黒2通りあるのでループ
    println!(
        "{}",
        solve(0, U_INF, 0, &vertexes, &mut dp) + solve(0, U_INF, 1, &vertexes, &mut dp)
    );
}

fn solve(
    now: usize,
    parent: usize,
    color: usize,
    vertexes: &Vec<Vec<usize>>,
    dp: &mut Vec<Vec<Option<ModUsize>>>,
) -> ModUsize {
    match dp[now][color] {
        Some(t) => t,
        None => {
            let mut cnt = ModUsize::new(1);
            //今の色に応じて白だけor白と黒両方見る
            let next_colors = if color == 1 { &[0][..] } else { &[0, 1][..] };
            //今の頂点とつながっている頂点のうち親でないもの全てに対して
            for &v in &vertexes[now] {
                if v == parent {
                    continue;
                } else {
                    let mut tmp = ModUsize::new(0);
                    //再帰
                    for &c in next_colors {
                        tmp += solve(v, now, c, vertexes, dp);
                    }
                    cnt *= tmp;
                }
            }
            dp[now][color] = Some(cnt);
            cnt
        }
    }
}

use num_integer::Integer;
use smallvec::alloc::fmt::{Display, Formatter};
use std::fmt;
use std::ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Sub, SubAssign};

#[derive(Copy, Clone)]
pub struct ModUsize {
    pub mod_value: usize,
    pub value: usize,
}

impl ModUsize {
    pub fn new(n: usize) -> Self {
        Self {
            mod_value: Self::mod1(),
            value: n % Self::mod1(),
        }
    }

    pub fn pow(self, n: usize) -> Self {
        if n == 0 {
            Self::new(1)
        } else if n % 2 == 0 {
            let t = self.pow(n / 2);
            t * t
        } else {
            self * self.pow(n - 1)
        }
    }

    pub fn inv(self) -> Self {
        self.pow(self.mod_value - 2)
    }

    pub fn mod1() -> usize {
        1000000007
    }

    pub fn mod2() -> usize {
        998244353
    }
}

impl Add for ModUsize {
    type Output = ModUsize;

    fn add(self, rhs: Self) -> Self::Output {
        let mut tmp = self;
        tmp.value += rhs.value;
        if tmp.value >= self.mod_value {
            tmp.value -= self.mod_value;
        }
        tmp
    }
}

impl AddAssign for ModUsize {
    fn add_assign(&mut self, rhs: Self) {
        *self = *self + rhs;
    }
}

impl Sub for ModUsize {
    type Output = ModUsize;

    fn sub(self, rhs: Self) -> Self::Output {
        let mut tmp = self;
        if tmp.value < rhs.value {
            tmp.value += self.mod_value;
        }
        tmp.value -= rhs.value;
        tmp
    }
}

impl SubAssign for ModUsize {
    fn sub_assign(&mut self, rhs: Self) {
        *self = *self - rhs;
    }
}

impl Mul for ModUsize {
    type Output = ModUsize;

    fn mul(self, rhs: Self) -> Self::Output {
        let mut tmp = self;
        tmp.value *= rhs.value;
        tmp.value %= self.mod_value;
        tmp
    }
}

impl MulAssign for ModUsize {
    fn mul_assign(&mut self, rhs: Self) {
        *self = *self * rhs;
    }
}

impl Div for ModUsize {
    type Output = ModUsize;

    fn div(self, rhs: Self) -> Self::Output {
        let mut tmp = self;
        tmp.value /= rhs.value;
        tmp.value %= self.mod_value;
        tmp
    }
}

impl DivAssign for ModUsize {
    fn div_assign(&mut self, rhs: Self) {
        *self = *self / rhs;
    }
}

impl Display for ModUsize {
    fn fmt(&self, f: &mut Formatter<'_>) -> fmt::Result {
        write!(f, "{}", self.value)
    }
}