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 PHP7 (7.0.15) (judge verdict: Wrong Answer)

<?php
list($N, $M) = ints();

$uft = new UFT($N+$M);
for($i = 1; $i <= $N; $i++){
    $l = ints();
    array_shift($l);
    foreach($l as $ll){
        $uft->unite($i, $ll);
    }
}
for($i = 1; $i <= $N; $i++){
    $r[] = $uft->getRoot($i);
}
echo (min($r) == max($r)) ? "YES" : "NO";

class UFT{
    public $parent;
    public $size;
    public $rank;
    public function __construct($size){
        for($i = 1; $i <= $size; $i++){
            $this->size[$i] = 1;
            $this->rank[$i] = 1;
            $this->parent[$i] = 0;
        }
    }
    public function dump(){
        o("--------------");
        o($this->parent);
        o($this->size);
        o($this->rank);
    }
    public function getRoot($i){
        if($this->parent[$i] == 0){
            return $i;
        }else{
            return $this->getRoot($this->parent[$i]);
        }
    }
    public function unite($i, $j){
        $rootI = $this->getRoot($j);
        $rootJ = $this->getRoot($i);
        if($rootJ == $rootI)return false;//元から同じグループ
        if($this->rank[$rootI] > $this->rank[$rootJ])list($rootI, $rootJ) = [$rootJ, $rootI];//Rank(J)>Rank(I)に揃えておく
        $this->parent[$rootI] = $rootJ;
        if($this->rank[$rootI] == $this->rank[$rootJ]){
            $this->rank[$rootJ]++;
        }
        $this->size[$rootJ]+=$this->size[$rootI];
        $this->size[$rootI] = '*';//不要な情報となるので潰す/デバッグ出力向けに*を入れている
        $this->rank[$rootI] = '*';//同上
    }
    public function size($i){return $this->size[$this->getRoot($i)];}
    public function isUnion($i, $j){return $this->getRoot($i) == $this->getRoot($j);}
}

function str(){return trim(fgets(STDIN));}
function ints($n = false){
  if($n===false){
    return array_map('intval',explode(' ',trim(fgets(STDIN))));
  }else{$ret = [];for($i = 0; $i < $n; $i++)foreach(array_map('intval',explode(' ',trim(fgets(STDIN)))) as $j => $v)$ret[$j][] = $v;return $ret;}
}
function int(){return intval(trim(fgets(STDIN)));}
function chmax(&$a,$b){if($a<$b){$a=$b;return 1;}return 0;}
function chmin(&$a,$b){if($a>$b){$a=$b;return 1;}return 0;}
function popcount($x){$c=0;while($x){$x&=$x-1;++$c;}return$c;}
function o(...$val){
    if(count($val)==1)$val=array_shift($val);
    echo debug_backtrace()[0]['line'].")";
    if(is_array($val)){
        if(count($val) == 0)echo "empty array";
        elseif(!is_array(current($val)))echo "array: ",implode(" ", addIndex($val)),"\n";
        else{
            echo "array:array\n";
            if(isCleanArray($val))foreach($val as $row)echo implode(" ", addIndex($row)),"\n";
            else foreach($val as $i => $row)echo "[".$i."] ".implode(" ", addIndex($row)),"\n";
        }
    }else echo $val."\n";
}
function addIndex($val){if(!isCleanArray($val)){$val = array_map(function($k, $v){return $k.":".$v;}, array_keys($val), $val);}return $val;}
function isCleanArray($array){$clean=true;$i = 0;foreach($array as $k=>$v){if($k != $i++)$clean = false;}return $clean;}
// 座圧対象の配列 -> [圧縮された配列,復元用のMap,圧縮用のMap]
function atsu($array){$a = array_flip($array);$fuku=array_flip($a);sort($fuku);$atsu = array_flip($fuku);foreach($array as $i=>$val)$array[$i]=$atsu[$val];return [$array, $fuku, $atsu];}
function gcdAll($array){$gcd=$array[0];for($i=1,$I=count($array);$i<$I;++$i){$gcd=gcd($gcd,$array[$i]);}return $gcd;}
function gcd($m, $n){if(!$n)return $m;return gcd($n, $m % $n);}
function lcmAll($array){$lcm=$array[0];for($i=1,$I=count($array);$i<$I;++$i){$lcm=lcm($lcm,$array[$i]);}return $lcm;}
function lcm($a, $b) {return $a / gcd($a, $b) * $b;}

function dfs($current, $from = -1, $d = 0){
  global $G, $distance;
  $distance[$current] = $d;
  foreach($G[$current] as $to){
    if($from != $to){
      dfs($to, $current, $d + 1);
    }
  }
}

function loadTree($N = false){
  if($N === false)$N = $GLOBALS['N'];
  return loadGraph($N, $N-1);
}
function loadGraph($N = false, $M = false, $both = true){
  if($N === false)$N = $GLOBALS['N'];
  if($M === false)$M = $GLOBALS['M'];
  $G = array_fill(1, $N, []);
  for($i = 0; $i < $M; $i++){
    $values = ints();
    if(count($values) == 2){
      list($a, $b) = $values;
      $G[$a][] = $b;
      if($both)$G[$b][] = $a;
    }else{
      list($a, $b, $d) = $values;
      $G[$a][] = [$b, $d];
      if($both)$G[$b][] = [$a, $d];
    }
  }
  return $G;
}