Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

A. Bulbs

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputVasya wants to turn on Christmas lights consisting of *m* bulbs. Initially, all bulbs are turned off. There are *n* buttons, each of them is connected to some set of bulbs. Vasya can press any of these buttons. When the button is pressed, it turns on all the bulbs it's connected to. Can Vasya light up all the bulbs?

If Vasya presses the button such that some bulbs connected to it are already turned on, they do not change their state, i.e. remain turned on.

Input

The first line of the input contains integers *n* and *m* (1 ≤ *n*, *m* ≤ 100) — the number of buttons and the number of bulbs respectively.

Each of the next *n* lines contains *x*_{i} (0 ≤ *x*_{i} ≤ *m*) — the number of bulbs that are turned on by the *i*-th button, and then *x*_{i} numbers *y*_{ij} (1 ≤ *y*_{ij} ≤ *m*) — the numbers of these bulbs.

Output

If it's possible to turn on all *m* bulbs print "YES", otherwise print "NO".

Examples

Input

3 4

2 1 4

3 1 3 1

1 2

Output

YES

Input

3 3

1 1

1 2

1 1

Output

NO

Note

In the first sample you can press each button once and turn on all the bulbs. In the 2 sample it is impossible to turn on the 3-rd lamp.

Codeforces (c) Copyright 2010-2018 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: May/27/2018 00:17:57 (d3).

Desktop version, switch to mobile version.

User lists

Name |
---|