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)]
use std::cmp::*;
#[allow(unused_imports)]
use std::collections::*;

fn main(){
    let (n, m): (usize, usize) = readln();
    let mut exists: Vec<bool> = vec![false;m];
    let mut uf = UnionFind::new(m);
    for _ in 0..n {
        let xs: Vec<usize> = readln();
        let k = xs[0];
        let x = xs[1] - 1;
        exists[x] = true;
        for i in 2..k+1 {
            exists[xs[i]-1] = true;
            uf.unite(x, xs[i]-1);
        }
    }

    let mut origin = 0;
    for i in 0..m {
        if exists[i] {
            origin = i;
            break;
        }
    }

    for i in 0..m {
        if uf.equiv(origin, i) || !exists[i]{
            continue;
        } else {
            println!("NO");
            return;
        }
    }
    println!("YES");
}


#[allow(dead_code)]
fn get_line() -> String{
    let mut buf = String::new();
    std::io::stdin().read_line(&mut buf).unwrap();
    buf.trim_right().to_string()
}

#[allow(dead_code)]
fn get_chars() -> Vec<char>{
    get_line().chars().collect()
}

#[allow(dead_code)]
fn readln<T: Read>() -> T{
    let mut buf = String::new();
    std::io::stdin().read_line(&mut buf).unwrap();
    T::read(buf.trim_right())
}

trait Read{
    fn read(s: &str) -> Self;
}

macro_rules! read_impl{
    ($($t:ty)*) => ($(
        impl Read for $t {
            fn read(s: &str) -> $t{
                s.parse().unwrap()
            }
        }
    )*)
}
read_impl! { usize u8 u16 u32 u64 isize i8 i16 i32 i64 f32 f64 }

impl<T: Read> Read for Vec<T>{
    fn read(s: &str) -> Self {
        s.split_whitespace().map(T::read).collect()
    }
}

impl<A: Read, B: Read> Read for (A, B){
    fn read(s: &str) -> Self {
        let tokens: Vec<_> = s.split_whitespace().collect();
        (A::read(tokens[0]), B::read(tokens[1]))
    }
}

impl<A: Read, B: Read, C: Read> Read for (A, B, C){
    fn read(s: &str) -> Self {
        let tokens: Vec<_> = s.split_whitespace().collect();
        (A::read(tokens[0]), B::read(tokens[1]), C::read(tokens[2]))
    }
}

struct UnionFind{
    parent: Vec<usize>,
    rank: Vec<usize>
}

impl UnionFind{
    fn new(n: usize) -> UnionFind{
        let mut parent: Vec<usize> = Vec::with_capacity(n);
        for i in 0..n{
            parent.push(i)
        }
        UnionFind{parent: parent, rank: vec![0; n]}
    }

    fn find(&mut self, x: usize) -> usize{
        if self.parent[x] == x {
            x
        } else {
            let px = self.parent[x];
            let root = self.find(px);
            self.parent[x] = root;
            root
        }
    }

    fn unite(&mut self, x: usize, y: usize){
        let px = self.find(x);
        let py = self.find(y);

        if px == py {return}

        if self.rank[px] < self.rank[py] {
            self.parent[px] = py;
        } else {
            self.parent[py] = px;
            if self.rank[px] == self.rank[py] {
                self.rank[px] += 1;
            }
        }

    }

    #[allow(dead_code)]
    fn equiv(&mut self, x: usize, y: usize) -> bool{
        self.find(x) == self.find(y)
    }

}