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_macros)]
macro_rules! read {
    ([$t:ty] ; $n:expr) => {
        (0..$n).map(|_| read!([$t])).collect::<Vec<_>>()
    };
    ($($t:ty),+ ; $n:expr) => {
        (0..$n).map(|_| read!($($t),+)).collect::<Vec<_>>()
    };
    ([$t:ty]) => {{
        rl()
            .split_whitespace()
            .map(|word| word.parse().unwrap())
            .collect::<Vec<$t>>()
    }};
    ($t:ty) => {
        rl().parse::<$t>().unwrap()
    };
    ($($t:ty),*) => {{
        let buf = rl();
        let mut w = buf.split_whitespace().into_iter();
        ($(w.next().unwrap().parse::<$t>().unwrap()),*)
    }};
}

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

pub fn recurse<X, Y, F: FnMut(&mut FnMut(X) -> Y, X) -> Y>(x: X, mut f: F) -> Y {
    fn call<X, Y>(x: X, f: &mut FnMut(&mut FnMut(X) -> Y, X) -> Y) -> Y {
        let fp = f as *mut FnMut(&mut FnMut(X) -> Y, X) -> Y;
        let f1 = unsafe { &mut *fp };
        let f2 = unsafe { &mut *fp };
        f1(&mut |x: X| call(x, f2), x)
    }
    call(x, &mut f)
}

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

    let mut done = vec![false; N + M];
    recurse(0, |go, v| {
        if done[v] {
            return;
        }
        done[v] = true;
        for &w in g[v].iter() {
            go(w);
        }
    });

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