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 C (GCC 5.4.1) (judge verdict: Accepted)

/*
cat <<EOF >mistaken-paste
*/

#pragma GCC diagnostic ignored "-Wincompatible-pointer-types"

#include <stdio.h>
#include <stdint.h>
#include <stdlib.h>
#include <string.h>
#include <stdbool.h>
#include <math.h>

#define BIG 2000000007
#define VERYBIG 200000000000007LL

#define MOD 1000000007
typedef uint64_t ull;
typedef  int64_t sll;

#define N_MAX 200000
#define M_MAX 100000

#ifdef __cplusplus
#include <queue>
#include <stack>
// #include <tuple>
#include <functional>

using namespace std; // I'm NOT gonna use C++ without compro. shit

typedef priority_queue<ull, vector<ull>, greater<ull> > upque123;
typedef priority_queue<ull, vector<ull> > upque321;
typedef priority_queue<sll, vector<sll>, greater<sll> > spque123;
typedef priority_queue<sll, vector<sll> > spque321;

#endif

typedef struct {
	int32_t a;
	int32_t b;
} hw;

typedef struct {
	sll a;
	sll b;
} hwll;

typedef struct {
	hwll a;
	hwll b;
} linell;


typedef struct {
	ull s;
	ull t;
	int32_t c;
} struct_a;

typedef struct {
	int32_t from;
	int32_t to;
	sll cost;
} struct_b;



const hw vector8[8] = {
	{-1, -1},
	{-1,  0},
	{-1, +1},
	{ 0, -1},
	{ 0, +1},
	{+1, -1},
	{+1,  0},
	{+1, +1}
};

ull n, m;
ull h, w;
ull k;
ull q;
ull vua, vub, vuc, vud, vue, vuf;
sll vsa, vsb, vsc, vsd, vse, vsf;
long double vra, vrb, vrc;
double vda, vdb, vdc;
size_t slen;
size_t tlen;
char ch, dh;

void swap_adj (ull *a, ull *b) {
	if (*a != *b) {
		ull tmp = *b;
		*b = *a;
		*a = tmp;
	}
	return;
}

int32_t digits (ull x) {
	int32_t i = 1;
	while (x >= 10) {
		x /= 10;
		i++;
	}
	return i;
}

ull umin (ull x, ull y) {
	return (x < y) ? x : y;
}

ull umax (ull x, ull y) {
	return (x > y) ? x : y;
}

sll smin (sll x, sll y) {
	return (x < y) ? x : y;
}

sll smax (sll x, sll y) {
	return (x > y) ? x : y;
}

ull gcd (ull x, ull y) {
	if (x < y) {
		return gcd(y, x);
	} else if (y == 0) {
		return x;
	} else {
		return gcd(y, x % y);
	}
}

ull bitpow (ull a, ull x, ull modulo) {
	ull result = 1;
	while (x) {
		if (x & 1) {
			result *= a;
			result %= modulo;
		}
		x /= 2;
		a = (a * a) % modulo;
	}
	return result;
}

ull divide (ull a, ull b, ull modulo) {
	return (a * bitpow(b, modulo - 2, modulo)) % modulo;
}

ull ullabs (ull a, ull b) {
	if (a >= b) {
		return a - b;
	} else {
		return b - a;
	}
}

sll sllabs (sll a, sll b) {
	if (a >= b) {
		return a - b;
	} else {
		return b - a;
	}
}

sll nibutanlobo (bool (*func)(sll arg), sll ok, sll ng) {
	while (sllabs(ok, ng) > 1) {
		sll med = (ok + ng) / 2;
		if (func(med)) {
			ok = med;
		} else {
			ng = med;
		}

		// printf("debug: [%lld %lld)\n", ok, ng);
	}

	if (!func(ok)) return ok * 2 - ng;
	return ok;
}

void printUquotient (ull left, ull right) {
	const int32_t digits = 20;

	printf("%llu.", left / right);
	left %= right;
	for (int32_t i = 0; i < digits; i++) {
		left *= 10;
		printf("%1d", left / right);
		left %= right;
	}
	puts("");

	return;
}

void printSquotient (sll left, sll right) {
	if (left * right < 0) putchar('-');
	printUquotient(sllabs(left, 0), sllabs(right, 0));

	return;
}

int bitcount (ull n) {
	int result = 0;
	while (n) {
		if (n & 1) result++;
		n /= 2;
	}
	return result;
}

#ifdef __cplusplus

typedef struct {
	int32_t to;
	sll cost;
} edge;
typedef pair<sll, int32_t> P;

std::vector<edge> g[N_MAX];
void dijk_init (ull n, struct_b arr[]) {
	edge x;
	for (int32_t i = 0; i < n; i++) {
		x.to = arr[i].to;
		x.cost = arr[i].cost;
		g[arr[i].from].push_back(x);
	}
}

bool dijkstra (int s, sll distance[]) {
	priority_queue<P, std::vector<P>, greater<P> > que; // (最短距離, 頂点番号)
	que.push(P(distance[s], s));

	bool ischanged = false;
	while (!que.empty()) {
		P p = que.top();
		que.pop();

		sll v = p.second;
		if (distance[v] < p.first) continue;

		int32_t maxsize = g[v].size();
		for (int32_t i = 0; i < maxsize; i++) {
			edge e = g[v][i];
			if (distance[e.to] > distance[v] + e.cost) {
				distance[e.to] = distance[v] + e.cost;
				ischanged = true;
				que.push(P(distance[e.to], e.to));
			}
		}
	}

	return ischanged;
}

#endif

// sll dist[N_MAX];
// struct_b path[M_MAX * 2];

// ull a[N_MAX];
// ull a[M_MAX];
sll a[N_MAX];
// ull a[N_MAX][N_MAX];
// sll a[N_MAX][N_MAX];
// ull b[N_MAX];
// ull b[M_MAX];
// sll b[N_MAX];
// ull c[N_MAX];
// sll c[M_MAX];
// char c[N_MAX];
// char s[N_MAX + 1];
// char s[N_MAX + 1][N_MAX + 1];
// char s[N_MAX + 1][M_MAX + 1];
// char t[N_MAX + 1];

// ull alphabets[26];
// char alphabets[26];

// ull dp[N_MAX + 1];
// sll dp[N_MAX + 1];
// ull dp[N_MAX + 1][N_MAX + 1];
// sll dp[N_MAX + 1][N_MAX + 1];
// bool dp[N_MAX + 1];
// bool dp[N_MAX + 1][N_MAX + 1];
hwll arr[N_MAX];
// hwll arr[M_MAX];
// hwll brr[M_MAX];

ull l[M_MAX];
ull langindex[N_MAX];
ull langnum[N_MAX];

// typedef tuple<sll, int32_t, int32_t> P2d;



double distance (sll x1, sll y1, sll x2, sll y2) {
	double xdist2, ydist2, origindist, dist;

	xdist2 = (x1 - x2) * (x1 - x2);
	ydist2 = (y1 - y2) * (y1 - y2);
	return sqrt(xdist2 + ydist2);
}

int32_t pullcomp (const void *left, const void *right) {
	ull l = *(ull*)left;
	ull r = *(ull*)right;
	if (l < r) {
		return -1;
	}
	if (l > r) {
		return +1;
	}
	return 0;
}

int32_t phwllABcomp (const void *left, const void *right) {
	hwll l = *(hwll*)left;
	hwll r = *(hwll*)right;
	if (l.a < r.a) {
		return -1;
	}
	if (l.a > r.a) {
		return +1;
	}
	if (l.b < r.b) {
		return -1;
	}
	if (l.b > r.b) {
		return +1;
	}
	return 0;
}

ull rank[N_MAX + M_MAX];
ull parent[N_MAX + M_MAX];

ull uf_init (ull n) {
	sll i;
	for (i = 0; i < n; i++) {
		rank[i] = 0;
		parent[i] = i;
	}
	return n;
}

ull uf_find (ull x) {
	if (parent[x] == x) return x;
	return parent[x] = uf_find(parent[x]);
}

ull uf_union (ull a, ull b) {
	ull ap = uf_find(a);
	ull bp = uf_find(b);
	if (ap == bp) return ap;

	if (rank[ap] > rank[bp]) {
		parent[bp] = ap;
	} else {
		parent[ap] = bp;
		if (rank[ap] == rank[bp]) {
			rank[bp]++;
		}
	}
	return ap;
}

ull solve () {
	sll i, j, ki;
	ull result = 0;
	// sll result = 0;
	// double result = 0;
	ull maybe = 0;
	// sll maybe = 0;
	ull sum = 0;
	// sll sum = 0;
	ull item;
	ull *dpcell;
	// 比較関数ぐらい即席で書け

	for (i = 0; i < n; i++) {
		scanf("%llu", &langnum[i]);
		langindex[i] = (i ? (langindex[i - 1] + langnum[i - 1]) : 0);

		for (j = 0; j < langnum[i]; j++) {
			ull x;
			scanf("%llu", &x);
			x--;
			l[langindex[i] + j] = x;
		}
	}
	const ull lsum = langindex[n - 1] + langnum[n - 1];

	j = 0;
	for (i = 0; i < lsum; i++) {
		if (j < n - 1 && i >= langindex[j + 1]) j++;

		arr[i].a = l[i];
		arr[i].b = j;
		// printf("%llu: %llu/%llu\n", i, l[i], j);
	}
	qsort(arr, lsum, sizeof(hwll), phwllABcomp);

	// uf_init(n);
	// // printf("%lld: %llu/%llu\n", 0ULL, arr[0].a, arr[0].b);
	// for (i = 1; i < lsum; i++) {
	// 	// printf("%llu: %llu/%llu\n", i, arr[i].a, arr[i].b);
	// 	if (arr[i].a == arr[i - 1].a) {
	// 		// printf("%llu and %lld united\n", arr[i].b, arr[i - 1].b);
	// 		uf_union(arr[i].b, arr[i - 1].b);
	// 	}
	// }

	// // printf("%lld: %llu\n", 0ULL, uf_find(0));
	// for (i = 1; i < n; i++) {
	// 	// printf("%lld: %llu\n", i, uf_find(i));
	// 	if (uf_find(i) != uf_find(i - 1)) goto fail;
	// }
	// goto success;

	uf_init(n + lsum);
	j = 0;
	for (i = 0; i < lsum; i++) {
		if (j < n - 1 && i >= langindex[j + 1]) j++;
		uf_union(j, n + l[i]);
	}

	for (i = 1; i < n; i++) {
		if (uf_find(i - 1) != uf_find(i)) goto fail;
	}
	goto success;

	// printf("%llu\n", result);
	// printf("%.12lf\n", (double)result);
	// puts(s);

	return 0;

	success:
	puts("YES");
	// puts("Yes");
	// printf("%llu\n", result);
	// puts("0");
	// puts("CONTINUE");
	return 0;

	fail:
	puts("NO");
	// puts("No");
	// puts("0");
	// puts("-1");
	// puts("-1 -1 -1");
	// puts("Impossible");
	return 1;
}

int32_t main (void) {
	int32_t i, j;
	int32_t x, y;

	// scanf("%lf%lf", &vda, &vdb);
	// scanf("%lld%lld%lld%lld", &vsa, &vsb, &vsc, &vsd);
	// scanf("%llu%llu", &vua, &vub, &vuc, &vud);
	// scanf("%llu%llu", &h, &w);
	scanf("%llu%llu", &n, &m);
	// scanf("%*llu");
	// scanf("%llu", &k, &m, &n);
	// scanf("%llu%llu%llu%llu%llu", &vua, &vub, &vuc, &vud, &vue, &vuf);
	// scanf("%lld", &vsa, &vsb, &vsc);
	// scanf("%s", s);
	// scanf("%s", t);
	// scanf("%llu", &m);
	// scanf("%llu", &q);
	// for (i = 0; i < n; i++) {
	// 	scanf("%llu", &a[i]);
	// 	// a[i]--;
	// }
	// for (i = 0; i < n; i++) {
	// 	scanf("%llu", &b[i]);
	// }
	// for (i = 0; i < h; i++) {
	// 	scanf("%llu", &a[i]);
	// }

	// for (i = 0; i < w; i++) {
	// 	scanf("%llu", &b[i]);
	// }	
	// for (i = 0; i < m; i++) {
	// 	scanf("%llu", &b[i]);
	// }
	// for (i = 0; i < h; i++) {
	// 	scanf("%s", s[i]);
	// }
	// scanf("%s", t);
	// for (i = 0; i < n; i++) {
	// 	scanf("%lld", &a[i]);
	// 	scanf("%lld", &b[i]);
	// 	// scanf("%llu", &c[i]);
	// 	// arr[i].a--;
	// 	// arr[i].b--;
	// 	// a[i]--;
	// 	// b[i]--;
	// }
	// for (i = 0; i < m; i++) {
	// 	scanf("%llu%llu", &arr[i].a, &arr[i].b);
	// 	arr[i].a--;
	// 	arr[i].b--;
	// }
	// for (i = 0; i < k; i++) {
	// 	scanf("%llu%llu", &brr[i].a, &brr[i].b);
	// 	brr[i].a--;
	// 	brr[i].b--;
	// }
	// for (i = 0; i < m; i++) {
	// 	for (j = 0; j < m; j++) {
	// 		scanf("%llu", &a[i][j]);
	// 	}
	// }
	// for (i = 0; i < n; i++) {
	// 	scanf("%llu%llu%llu", &a[i], &b[i], &c[i]);
	// }

	// scanf("%llu", &q);
	// scanf("%llu", &k);
	// k--;
	// for (i = 0; i < q; i++) {
	// 	scanf("%llu%llu", &a[i], &b[i]);
	// 	a[i]--;
	// 	b[i]--;
	// 	// solve();
	// }

	// for (i = 0; i < m; i++) {
	// 	scanf("%llu%llu", &arr[i].a, &arr[i].b);
	// 	arr[i].a--;
	// 	arr[i].b--;
	// }
	// for (i = 0; i < n; i++) {
	// 	for (j = 0; j < m; j++) {
	// 		scanf("%llu", &a[i][j]);
	// 		a[i][j]--;
	// 	}
	// }

	solve();

	// for (i = 0; i < m; i++) {
	// 	scanf("%llu%llu%llu", &vua, &vub, &vuc);
	// 	// scanf("%s%s", s, t);
	// 	// scanf("%f%f%f", &vda, &vdb, &vdc);
	// 	// scanf("%s", s);
	// 	solve();
	// }

	// while (scanf("%llu%llu", &n, &k), n + k) {
	// 	for (i = 0; i < n; i++) {
	// 		scanf("%llu", &a[i]);
	// 	}
	// 	solve();
	// }

	return 0;
}