Team Formation

You are given an integer $N$ representing the number of students and an integer $K$ representing the team size. Each student is assigned a unique number from $1$ to $N$. For each student, you are provided a list of preferred teammates. A student $i$ (with $1 \leq i \leq N$) prefers student $j$ if $j$ appears in $i$'s list. Your task is to determine whether there exists a team consisting of exactly $K$ students such that for every pair of distinct students in the team, each student prefers the other. If such a team exists, print "YES"; otherwise, print "NO".


Note: The preference list for each student may contain any number of distinct student numbers in the range $[1, N]$, and the input guarantees that students are numbered starting at $1$.

inputFormat

The first line contains two space-separated integers $N$ and $K$.
Each of the next $N$ lines contains a space-separated list of integers, representing the preferred teammates for the corresponding student $i$ (1-indexed). There is at least one integer in each list.

outputFormat

Output a single line containing the string "YES" if there exists a valid team of $K$ students satisfying the condition; otherwise, output "NO".## sample

4 3
2 3
1 3
1 2
1 2

YES