Migrated from Lutece 810 Food Delivery

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Description

Recently, people who love take-out foods increased sharply, especially in UESTC ACM team. And the restaurant who would like deliver the foods has increased to $M$.

Today $N$ students in UESTC ACM team wants take-out foods. Each student would like to eat foods from restaurant $a_i$ or $b_i$. However, the restaurant will deliver the foods if and only if the number of students that ordered its foods is not less than $2$.

Now we want to know whether there is a way to satisfied everyone's need.

Input

The first line of the input contains an integer $N, M$ ($1\leq N\leq 100, 1\leq M\leq 50$), as described above.

The next $N$ lines contain $2$ integers $a_i, b_i$ ($1\leq a_i, b_i\leq M$ and $a_i\neq b_i$) , indicating the first and the second restaurant's food the $ith$ student wants to have.

Output

Output Yes if there is a way to satisfied everyone, otherwise output No.

Samples

2 2
1 2
1 2

Yes

3 3
1 2
2 3
1 3

No

Resources

the 12th UESTC Programming Contest Final