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 (1.42.0) (judge verdict: Accepted)

#![allow(unused_imports)]

// language: Rust(1.42.0)
// check available crates on AtCoder at "https://atcoder.jp/contests/language-test-202001"
// My Library Repositry is at "https://github.com/Loptall/sfcpl"

/*
    水コーダーになれてうれしいです
*/

// from std...
use std::cmp::{
    max, min, Ordering,
    Ordering::{Equal, Greater, Less},
    Reverse,
};
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};
use std::convert::TryInto;
use std::fmt;
use std::mem::swap;
use std::num::{NonZeroU32, ParseIntError};
use std::ops::{
    Add, AddAssign, BitAnd, BitAndAssign, BitOr, BitOrAssign, BitXor, BitXorAssign, Div, DivAssign,
    Index, IndexMut, Mul, MulAssign, Neg, Rem, RemAssign, Shl, ShlAssign, Shr, ShrAssign, Sub,
    SubAssign,
};
use std::process::exit;
use std::{f32, f64, i128, i16, i32, i64, i8, isize, u128, u16, u32, u64, u8, usize};

// Dep' crates are...
use itertools::*;
use itertools_num::*;
use lazy_static::lazy_static;
use maplit::{btreemap, btreeset, hashmap, hashset};
use num_bigint::{BigInt, BigUint};
use num_complex::Complex;
use num_integer::{binomial, gcd, lcm, multinomial, Integer};
use num_rational::Rational;
use num_traits::{
    clamp, one, pow, zero, Num, NumAssignOps, NumOps, One, Pow, Signed, Unsigned, Zero,
};
use permutohedron::Heap;
use proconio::{
    derive_readable, fastout, input, is_stdin_empty,
    marker::{Bytes, Chars, Isize1, Usize1},
};
use rand::random;

pub use visualize::*;
pub mod visualize {
    use itertools::*;
    pub trait Visualize {
        fn visualize(&self, split: &str);
        fn continuous(&self) {
            self.visualize("");
        }
        fn spaces(&self) {
            self.visualize(" ");
        }
        fn lines(&self) {
            self.visualize("\n");
        }
    }
    macro_rules ! impl_vis_for_sized {($ ($ t : ty ) ,+ ) => {$ (impl Visualize for $ t {fn visualize (& self , _split : & str ) {print ! ("{}" , self ) ; } } ) + } ; }
    impl_vis_for_sized! {usize , u8 , u16 , u32 , u64 , u128 , isize , i8 , i16 , i32 , i64 , i128 , String , & str , char }
    impl<T: std::fmt::Display> Visualize for [T] {
        fn visualize(&self, split: &str) {
            print!("{}", self.iter().join(split));
        }
    }
    #[test]
    fn fmt() {
        let a = 2;
        a.visualize("");
        let b = "str";
        b.visualize("");
        let c = vec![1, 2, 3];
        c.visualize(" ");
        c.visualize("\n");
    }
    /// macro to output answer improved to println
    /// this macro will print '\n' at the last.
    /// # Patterns
    /// `,`, it means one space, it formats the elements, which is before, space-split.
    /// And insert a space after the prefix, unless it is at last.
    /// `=>`, it means empty string, it formats the element, witch is before, without any split.
    /// And insert nothing between two element.
    /// `;`, it means newline(\n), it formats the element, witch is before, newline-split.
    /// And insert a newline after the prefix, unless it is at last.
    /// # Eample
    /// ```
    /// #[test]
    /// fn vis_test() {
    ///     let a = 1;
    ///     let b = 2;
    ///     let c = 3;
    ///     let v = vec!['a', 'b', 'c'];
    ///     // single element test ...
    ///     vis!(a); // 1\n
    ///     vis!(a,); // 1\n
    ///     vis!(a =>); // 1\n
    ///     vis!(a;); // 1\n
    ///     println!();
    ///     vis!(a + b); // 3\n
    ///     println!();
    ///     vis!(v); // a b c\n
    ///     vis!(v,); // a b c\n
    ///     vis!(v =>); // abc\n
    ///     vis!(v;); // a\nb\nc\n
    ///     println!();
    ///     // multi elements connected by common operater test ...
    ///     println!();
    ///     vis!(a, b); // 1 2\n
    ///     vis!(a, b, c); // 1 2 3\n
    ///     vis!(a, b, c;); // 1 2 3\n
    ///     println!();
    ///     vis!(a => b); // 12\n
    ///     vis!(a => b => c); // 123\n
    ///     vis!(a => b => c ,); // 123\n
    ///     println!();
    ///     vis!(a; b); // 1\n2\n
    ///     vis!(a; b; c); // 1\n2\n3\n
    ///     vis!(a; b; c =>); // 1\n2\n3\n
    ///     println!();
    ///     // multi elements connected by different operater test ...
    ///     vis!(a, b; c); // 1 2\n3\n
    ///     vis!(a; b, c); // 1\n2 3\n
    ///     vis!(a => b, c); // 12 3\n
    ///     vis!(a; b => c); // 1\n23\n
    ///     println!();
    ///     vis!(a, v); // 1 a b c\n;
    ///     vis!(a, v;); // 1 a\nb\nc\n;
    ///     vis!(a => v =>); // 1abc\n;
    ///     println!("\d");
    ///     // panic!()
    /// }
    /// ```
    #[macro_export]
    macro_rules ! vis {() => {println ! () ; } ; ($ last : expr ; ) => {$ last . lines () ; vis ! () } ; ($ last : expr => ) => {$ last . continuous () ; vis ! () ; } ; ($ last : expr $ (, ) ? ) => {$ last . spaces () ; vis ! () ; } ; ($ first : expr ; $ ($ rest : tt ) * ) => {$ first . lines () ; println ! () ; vis ! ($ ($ rest ) * ) ; } ; ($ first : expr => $ ($ rest : tt ) * ) => {$ first . continuous () ; vis ! ($ ($ rest ) * ) ; } ; ($ first : expr , $ ($ rest : tt ) * ) => {$ first . spaces () ; print ! (" " ) ; vis ! ($ ($ rest ) * ) ; } ; }
    #[test]
    fn vis_test() {
        let a = 1;
        let b = 2;
        let c = 3;
        let v = vec!['a', 'b', 'c'];
        vis!();
        vis!(a);
        vis!(a,);
        vis ! (a => );
        vis ! (a ; );
        println!();
        vis!(a + b);
        println!();
        vis!(v);
        vis!(v,);
        vis ! (v => );
        vis ! (v ; );
        println!();
        println!();
        vis!(a, b);
        vis!(a, b, c);
        vis ! (a , b , c ; );
        println!();
        vis ! (a => b );
        vis ! (a => b => c );
        vis ! (a => b => c , );
        println!();
        vis ! (a ; b );
        vis ! (a ; b ; c );
        vis ! (a ; b ; c => );
        println!();
        vis ! (a , b ; c );
        vis ! (a ; b , c );
        vis ! (a => b , c );
        vis ! (a ; b => c );
        println!();
        vis!(a, v);
        vis ! (a , v ; );
        vis ! (a => v => );
    }
}

pub use consts::*;
pub mod consts {
    pub const MOD10E9_7: usize = 1000000007; // 10 ^ 9 + 7
    pub const MOD99_: usize = 998244353;
    pub const MAX: usize = std::usize::MAX; // = 2 ^ 64 - 1 = 18446744073709551615 ≈ 1.8 * 10 ^ 19
    pub const INF: usize = 2000000000000000000; // MAX / 9 < 2 * 10e18 < MAX / 10
    pub const FNI: i64 = -2000000000000000000; // == -(INF as i64)
    pub const PI: f64 = std::f64::consts::PI; // 3.141592653589793 -- 10 ^ -15
    pub const ASCII_A_LARGE: u8 = 65;
    pub const ASCII_A_SMALL: u8 = 97;
    pub const ASCII_0: u8 = 48;
    pub const ADJ4: &[(isize, isize); 4] = &[(1, 0), (0, 1), (-1, 0), (0, -1)];
    pub const ADJ8: &[(isize, isize); 8] = &[
        (1, 0),
        (1, 1),
        (0, 1),
        (-1, 1),
        (-1, 0),
        (-1, -1),
        (0, -1),
        (1, -1),
    ];
}
// code...
// #[fastout]
fn main() {
    input! {
        n: usize, m: usize,
        path: [(Usize1, Usize1); m]
    }

    let mut cnt = vec![true; n];
    for (a, b) in path {
        cnt[a] = !cnt[a];
        cnt[b] = !cnt[b];
    }

    if cnt.iter().all(|x| *x) {
        vis!("YES");
    } else {
        vis!("NO");
    }
}