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 Java8 (OpenJDK 1.8.0) (judge verdict: Runtime Error)

import java.util.*;
 
public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int H = sc.nextInt();
        int W = sc.nextInt();
        int[] num = new int[26];
        for (int i = 0; i < H; i++) {
            String s = sc.next();
            for (int j = 0; j < W; j++) {
                num[s.charAt(j)-'a']++;
            }
        }

        boolean ans = true;
        if (H%2 == 0 && W%2 == 0) {
            int num4 = H*W/4;
            for (int i = 0; i < 26; i++) {
                if (num[i] >= 4) {
                    int a = Math.min(num[i]/4, num4);
                    num[i] -= a*4;
                    num4 -= a;
                }
            }
            int others = 0;
            for (int i = 0; i < 26; i++) {
                others += num[i];
            }
            ans = others == 0;
        } else if (H%2 == 1 && W%2 == 1) {
            int num4 = (H-1)*(W-1)/4;
            for (int i = 0; i < 26; i++) {
                if (num[i] >= 4) {
                    int a = Math.min(num[i]/4, num4);
                    num[i] -= a*4;
                    num4 -= a;
                }
            }
            int num2 = (H-1)/2+(W-1)/2;
            for (int i = 0; i < 26; i++) {
                if (num[i] >= 2) {
                    int a = Math.min(num[i]/2, num2);
                    num[i] -= a*2;
                    num2 -= a;
                }
            }
            int others = 0;
            for (int i = 0; i < 26; i++) {
                others += num[i];
            }
            ans = others == 1;
        } else {
            int odd = H%2 == 1 ? H : W;
            int even = H%2 == 1 ? W : W;

            int num4 = (odd-1)*even/4;
            for (int i = 0; i < 26; i++) {
                if (num[i] >= 4) {
                    int a = Math.min(num[i]/4, num4);
                    num[i] -= a*4;
                    num4 -= a;
                }
            }
            int num2 = even/2;
            for (int i = 0; i < 26; i++) {
                if (num[i] >= 2) {
                    int a = Math.min(num[i]/2, num2);
                    num[i] -= a*2;
                    num2 -= a;
                }
            }
            int others = 0;
            for (int i = 0; i < 26; i++) {
                others += num[i];
            }
            ans = others == 0;
        }
        System.out.println(ans ? "Yes" : "No");
    }
}