Why did you book it without asking

Time limit1sMemory limit1024 MB

Summary

Given each member's list of attendable periods, the task is to check whether the reserved period X is in every list.

Level: Easy1 of 10
Topics: Implementation, Array
Solved: No attempts yet

Problem

Geonwoo became the team leader for a group project at Daejeon Science High School. To run the project, the team needs a classroom reserved at a period that every member can attend.

The classroom can only be used in $T$ fixed periods. Each period is written as a distinct integer from $1$ to $T$ .

Every member told Geonwoo which periods they can attend. Geonwoo reserved period $X$ without asking anyone. Can all members attend?

Input

The first line contains $T$ , the number of periods the classroom can be reserved for, and $X$ , the period Geonwoo reserved, separated by a space. $(1 \leq T \leq 1\,000;$ $1 \leq X \leq T)$

The second line contains $N$ , the number of team members. $(1 \leq N \leq 10)$

From the third line on, each member's available periods are given in two lines.

The first line contains $K_i$ , the number of periods member $i$ can attend. $(1 \leq K_i \leq T)$
The second line contains $K_i$ integers $A_{i,1}, A_{i,2}, \ldots, A_{i,K_i}$ , the periods member $i$ can attend, separated by spaces, in ascending order. $(1 \leq A_{i,1} < A_{i,2} < \cdots < A_{i,K_i} \leq T)$

All numbers in the input are positive integers.

Output

If all members can attend period $X$ , print YES. Otherwise, print NO.

Hint

Print YES or NO in all uppercase letters.

Examples2

Example 1

Input

12 5
7
5
2 3 5 7 11
4
5 7 10 12
3
4 5 7
6
1 3 5 7 11 12
12
1 2 3 4 5 6 7 8 9 10 11 12
2
5 7
9
1 3 5 6 7 8 9 10 11

Expected output

YES

Example 2

Input

7 3
4
1
4
6
1 2 4 5 6 7
3
1 3 4
2
4 7

Expected output

NO