Problem:
Score : 400 points

Problem Statement

On a planet far, far away, M languages are spoken. They are conveniently numbered 1 through M.

For CODE FESTIVAL 20XX held on this planet, N participants gathered from all over the planet.

The i-th (1≦i≦N) participant can speak K_i languages numbered L_{i,1}, L_{i,2}, ..., L_{i,{}K_i}.

Two participants A and B can communicate with each other if and only if one of the following conditions is satisfied:

There exists a language that both A and B can speak.

There exists a participant X that both A and B can communicate with.

Determine whether all N participants can communicate with all other participants.

Constraints

2≦N≦10^5

1≦M≦10^5

1≦K_i≦M

(The sum of all K_i)≦10^5

1≦L_{i,j}≦M

L_{i,1}, L_{i,2}, ..., L_{i,{}K_i} are pairwise distinct.

Partial Score

200 points will be awarded for passing the test set satisfying the following: N≦1000, M≦1000 and (The sum of all K_i)≦1000.

Additional 200 points will be awarded for passing the test set without additional constraints.

Input

The input is given from Standard Input in the following format:

N M
K_1 L_{1,1} L_{1,2} ... L_{1,{}K_1}
K_2 L_{2,1} L_{2,2} ... L_{2,{}K_2}
:
K_N L_{N,1} L_{N,2} ... L_{N,{}K_N}

Output

If all N participants can communicate with all other participants, print YES. Otherwise, print NO.

Sample Input 1

4 6
3 1 2 3
2 4 2
2 4 6
1 6

Sample Output 1

YES

Any two participants can communicate with each other, as follows:

Participants 1 and 2: both can speak language 2.

Participants 2 and 3: both can speak language 4.

Participants 1 and 3: both can communicate with participant 2.

Participants 3 and 4: both can speak language 6.

Participants 2 and 4: both can communicate with participant 3.

Participants 1 and 4: both can communicate with participant 2.

Note that there can be languages spoken by no participant.

Sample Input 2

4 4
2 1 2
2 1 2
1 3
2 4 3

Sample Output 2

NO

For example, participants 1 and 3 cannot communicate with each other.

Solution in Rust (1.15.1) (judge verdict: Accepted)

#![allow(unused_imports)]
#![allow(non_snake_case)]

use std::cmp::{max, min, Ordering};
use std::collections::*;
use std::io::*;
use std::ops::*;
use std::*;

// -----------------------------------------------
// Framework
// -----------------------------------------------

#[allow(unused)]
fn rl() -> String {
    let mut buf = String::new();
    io::stdin().read_line(&mut buf).unwrap();
    buf.trim_right().to_owned()
}

#[allow(unused)]
fn rw<T>() -> Vec<T>
where
    T: std::str::FromStr,
    T::Err: std::fmt::Debug,
{
    let mut buf = String::new();
    io::stdin().read_line(&mut buf).unwrap();
    buf.split_whitespace()
        .map(|word| T::from_str(word).unwrap())
        .collect()
}

trait IteratorExt: Iterator + Sized {
    fn vec(self) -> Vec<Self::Item> {
        self.collect()
    }
}

impl<T: Iterator> IteratorExt for T {}

#[allow(unused)]
macro_rules! debug {
    ($($arg:expr),*) => {
        #[cfg(debug_assertions)]
        {
            let entries = &[
                $((
                    &stringify!($arg).to_string() as &fmt::Debug,
                    &($arg) as &fmt::Debug,
                )),*
            ];
            eprintln!("{:?}", DebugMap(entries));
        }
    };
}

#[allow(unused)]
struct DebugMap<'a>(&'a [(&'a fmt::Debug, &'a fmt::Debug)]);

impl<'a> std::fmt::Debug for DebugMap<'a> {
    fn fmt(&self, fmt: &mut fmt::Formatter) -> fmt::Result {
        let mut m = fmt.debug_map();
        for &(key, value) in self.0.iter() {
            m.entry(key, value);
        }
        m.finish()
    }
}

// -----------------------------------------------
// Polyfill
// -----------------------------------------------

#[derive(PartialEq, Eq, Clone, Debug)]
pub struct Rev<T>(pub T);

impl<T: PartialOrd> PartialOrd for Rev<T> {
    fn partial_cmp(&self, other: &Rev<T>) -> Option<Ordering> {
        other.0.partial_cmp(&self.0)
    }
}

impl<T: Ord> Ord for Rev<T> {
    fn cmp(&self, other: &Rev<T>) -> Ordering {
        other.0.cmp(&self.0)
    }
}

#[allow(unused)]
macro_rules! eprintln {
    ($($arg:expr),*) => { _eprintln(format_args!($($arg),*)) }
}

fn _eprintln(args: fmt::Arguments) {
    let err = std::io::stderr();
    let mut err = err.lock();
    err.write_fmt(args).unwrap();
    err.write(b"\n").unwrap();
}

// -----------------------------------------------
// Solution
// -----------------------------------------------

pub fn main() {
    let w = rw::<usize>();
    let (N, M) = (w[0], w[1]);
    let mut g = vec![vec![]; N + M];
    for v in 0..N {
        let w = rw::<usize>();
        for &w in &w[1..] {
            g[v].push(N + w - 1);
            g[N + w - 1].push(v);
        }
    }

    fn dfs(v: usize, g: &Vec<Vec<usize>>, done: &mut Vec<bool>) {
        if done[v] {
            return;
        }
        done[v] = true;
        for &w in g[v].iter() {
            dfs(w, g, done);
        }
    }
    let mut done = vec![false; N + M];
    dfs(0, &g, &mut done);

    println!("{}", if (0..N).all(|v| done[v]) { "YES" } else { "NO" });
    return;
}

#[cfg(test)]
mod tests {
    use super::*;

    #[test]
    fn test_ok() {
        assert_eq!(7, 1 + 2 * 3);
    }
}