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 (1.15.1) (judge verdict: Accepted)

#[allow(unused_imports)]
use std::cmp::{Ordering};

#[allow(unused_imports)]
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};

#[allow(unused_imports)]
use std::io::{stdin, stdout, BufWriter, Write};

#[allow(unused_imports)]
use std::iter::FromIterator;

#[allow(unused_macros)]
macro_rules! min {
    ($x: expr) => ($x);
    ($x: expr, $($z: expr),+) => {{
        std::cmp::min($x, min!($($z),*))
    }}
}

#[allow(unused_macros)]
macro_rules! max {
    ($x: expr) => ($x);
    ($x: expr, $($z: expr),+) => {{
        std::cmp::max($x, max!($($z),*))
    }}
}

#[allow(unused_macros)]
macro_rules! get { 
    ([$t: ty]) => { 
        { 
            let mut line = String::new(); 
            stdin().read_line(&mut line).unwrap(); 
            line.split_whitespace().map(|t|t.parse::<$t>().unwrap()).collect::<Vec<_>>()
        }
    };
    ([$t: ty];$n: expr) => {
        (0..$n).map(|_|get!([$t])).collect::<Vec<_>>()
    };
    ($t: ty) => {
        {
            let mut line = String::new();
            stdin().read_line(&mut line).unwrap();
            line.trim().parse::<$t>().unwrap()
        }
    };
    ($($t: ty),*) => {
        { 
            let mut line = String::new();
            stdin().read_line(&mut line).unwrap();
            let mut iter = line.split_whitespace();
            ($(iter.next().unwrap().parse::<$t>().unwrap(),)*)
        }
    };
    ($t: ty; $n: expr) => {
        (0..$n).map(|_|get!($t)).collect::<Vec<_>>()
    };
    ($($t: ty),*; $n: expr) => {
        (0..$n).map(|_|get!($($t),*)).collect::<Vec<_>>()
    };
}

#[allow(unused_macros)]
macro_rules! debug {
    ($($a:expr),*) => {
        #[cfg(debug_assertions)]
        writeln!(&mut std::io::stderr(), concat!("[DEBUG] ", $(stringify!($a), "={:?} "),*), $($a),*).unwrap();
    }
}

const BIG_STACK_SIZE: bool = true;

#[allow(dead_code)]
fn main() {
    use std::thread;
    if BIG_STACK_SIZE {
        thread::Builder::new()
            .stack_size(32 * 1024 * 1024)
            .name("solve".into())
            .spawn(solve)
            .unwrap()
            .join()
            .unwrap();
    } else {
        solve();
    }
}

#[derive(Copy, Clone, PartialEq, Eq, PartialOrd, Ord)]
struct ModInt {
    value: usize,
}
impl ModInt {
    fn new(value: usize) -> Self {
        ModInt {
            value: value % Self::modulo(),
        }
    }
    fn value(&self) -> usize {
        self.value
    }
    fn modulo() -> usize {
        1_000_000_007
    }
}
impl From<usize> for ModInt {
    fn from(value: usize) -> Self {
        ModInt { value: value }
    }
}
impl std::ops::Add for ModInt {
    type Output = Self;
    fn add(self, other: Self) -> Self {
        let mut value = self.value + other.value;
        if value > Self::modulo() {
            value -= Self::modulo();
        }
        ModInt { value: value }
    }
}
impl std::ops::Sub for ModInt {
    type Output = Self;
    fn sub(self, other: Self) -> Self {
        let mut value = self.value;
        if value < other.value {
            value += Self::modulo();
        }
        value -= other.value;
        ModInt { value: value }
    }
}
impl std::ops::Mul for ModInt {
    type Output = Self;
    fn mul(self, other: Self) -> Self {
        let value = self.value * other.value % Self::modulo();
        ModInt { value: value }
    }
}
impl std::ops::Div for ModInt {
    type Output = Self;
    fn div(self, other: Self) -> Self {
        let mut exp = Self::modulo() - 2;
        let mut value = self.value;
        let mut ovalue = other.value;
        while exp > 0 {
            if exp % 2 == 1 {
                value = value * ovalue % Self::modulo();
            }
            ovalue = ovalue * ovalue % Self::modulo();
            exp /= 2;
        }
        ModInt { value: value }
    }
}
impl std::ops::AddAssign for ModInt {
    fn add_assign(&mut self, other: Self) {
        *self = *self + other;
    }
}
impl std::ops::SubAssign for ModInt {
    fn sub_assign(&mut self, other: Self) {
        *self = *self - other;
    }
}
impl std::ops::MulAssign for ModInt {
    fn mul_assign(&mut self, other: Self) {
        *self = *self * other;
    }
}
impl std::ops::DivAssign for ModInt {
    fn div_assign(&mut self, other: Self) {
        *self = *self / other;
    }
}
impl std::fmt::Debug for ModInt {
    fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
        write!(f, "{}", self.value)
    }
}
impl std::fmt::Display for ModInt {
    fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
        write!(f, "{}", self.value)
    }
}

fn dfs(node: usize, parent: usize, nodes: &Vec<Vec<usize>>, dp: &mut Vec<Vec<Option<ModInt>>>, color: usize) -> ModInt {
    if let Some(res) = dp[node][color] {
        return res;
    }

    let mut res = ModInt::new(1);
    for &next in &nodes[node] {
        if next == parent {
            continue;
        }
        if color == 0 {
            res *= dfs(next, node, nodes, dp, 0) + dfs(next, node, nodes, dp, 1);
        } else {
            res *= dfs(next, node, nodes, dp, 0);
        }
    }
    dp[node][color] = Some(res);
    res
}

fn solve() {
    let n = get!(usize);
    let xy = get!(usize, usize; n-1);

    let mut dp = vec![vec![None; 2]; n+1];
    let mut nodes = vec![Vec::new(); n+1];
    for (x,y) in xy {
        nodes[x].push(y);
        nodes[y].push(x);
    }
    let mut res = ModInt::new(0);
    for i in 0..2 {
        res += dfs(1, 0, &nodes, &mut dp, i);
    }
    println!("{}", res);
}