Problem:
Score : 500 points

Problem Statement

Takahashi is not good at problems about trees in programming contests, and Aoki is helping him practice.

First, Takahashi created a tree with N vertices numbered 1 through N, and wrote 0 at each edge.

Then, Aoki gave him M queries. The i-th of them is as follows:

Increment the number written at each edge along the path connecting vertices a_i and b_i, by one.

After Takahashi executed all of the queries, he told Aoki that, for every edge, the written number became an even number.
However, Aoki forgot to confirm that the graph Takahashi created was actually a tree, and it is possible that Takahashi made a mistake in creating a tree or executing queries.

Determine whether there exists a tree that has the property mentioned by Takahashi.

Constraints

2 ≤ N ≤ 10^5

1 ≤ M ≤ 10^5

1 ≤ a_i,b_i ≤ N

a_i ≠ b_i

Input

Input is given from Standard Input in the following format:

N M
a_1 b_1
:
a_M b_M

Output

Print YES if there exists a tree that has the property mentioned by Takahashi; print NO otherwise.

Sample Input 1

4 4
1 2
2 4
1 3
3 4

Sample Output 1

YES

For example, Takahashi's graph has the property mentioned by him if it has the following edges: 1-2, 1-3 and 1-4.
In this case, the number written at every edge will become 2.

Sample Input 2

5 5
1 2
3 5
5 1
3 4
2 3

Sample Output 2

NO

Solution in Rust (1.15.1) (judge verdict: Accepted)

#![allow(unused_imports)]
#![allow(dead_code)]
use std::cmp::*;
use std::collections::*;

const NOTHING: usize = std::usize::MAX;

fn main() {
    let (n, m): (usize, usize) = readln();
    let mut gr: Vec<Vec<(usize, usize)>> = vec![vec![];n];
    let mut src: Vec<usize> = vec![NOTHING;m];
    let mut dst: Vec<usize> = vec![NOTHING;m];
    let mut used: Vec<bool> = vec![false;m];
    for i in 0..m {
        let (a, b): (usize, usize) = readln();
        let a = a - 1;
        let b = b - 1;
        src[i] = a;
        dst[i] = b;
        gr[a].push((b, i));
        gr[b].push((a, i));
    }

    fn dfs(gr: &Vec<Vec<(usize, usize)>>, used: &mut Vec<bool>, cur: usize, goal: usize) -> bool {
        if cur == goal {
            return true;
        } else {
            for &(v, i) in &gr[cur] {
                if used[i] {
                    continue;
                } else {
                    used[i] = true;
                    return dfs(gr, used, v, goal);
                }
            }
            return false;
        }
    }

    for i in 0..m {
        if used[i] {
            continue;
        }
        used[i] = true;
        if dfs(&gr, &mut used, src[i], dst[i]) {
            continue;
        } else {
            println!("NO");
            return;
        }
    }
    println!("YES");

}


fn get_line() -> String {
    let mut buf = String::new();
    std::io::stdin().read_line(&mut buf).unwrap();
    buf.trim_right().to_string()
}

fn get_chars() -> Vec<char> {
    get_line().chars().collect()
}

fn readln<T: Read>() -> T {
    let mut buf = String::new();
    std::io::stdin().read_line(&mut buf).unwrap();
    T::read(buf.trim_right())
}

trait Read {
    fn read(s: &str) -> Self;
}

macro_rules! read_impl{
    ($($t:ty)*) => ($(
        impl Read for $t {
            fn read(s: &str) -> $t{
                s.parse().unwrap()
            }
        }
    )*)
}
read_impl! { usize u8 u16 u32 u64 isize i8 i16 i32 i64 f32 f64 }

impl<T: Read> Read for Vec<T> {
    fn read(s: &str) -> Self {
        s.split_whitespace().map(T::read).collect()
    }
}

impl<A: Read, B: Read> Read for (A, B) {
    fn read(s: &str) -> Self {
        let tokens: Vec<_> = s.split_whitespace().collect();
        (A::read(tokens[0]), B::read(tokens[1]))
    }
}

impl<A: Read, B: Read, C: Read> Read for (A, B, C) {
    fn read(s: &str) -> Self {
        let tokens: Vec<_> = s.split_whitespace().collect();
        (A::read(tokens[0]), B::read(tokens[1]), C::read(tokens[2]))
    }
}