We have N irregular jigsaw pieces. Each piece is composed of three rectangular parts of width 1 and various heights joined together. More specifically:

* The i-th piece is a part of height H, with another part of height A_i joined to the left, and yet another part of height B_i joined to the right, as shown below. Here, the bottom sides of the left and right parts are respectively at C_i and D_i units length above the bottom side of the center part.



<image>

Snuke is arranging these pieces on a square table of side 10^{100}. Here, the following conditions must be held:

* All pieces must be put on the table.
* The entire bottom side of the center part of each piece must touch the front side of the table.
* The entire bottom side of the non-center parts of each piece must either touch the front side of the table, or touch the top side of a part of some other piece.
* The pieces must not be rotated or flipped.



Determine whether such an arrangement is possible.

Constraints

* 1 \leq N \leq 100000
* 1 \leq H \leq 200
* 1 \leq A_i \leq H
* 1 \leq B_i \leq H
* 0 \leq C_i \leq H - A_i
* 0 \leq D_i \leq H - B_i
* All input values are integers.

Input

Input is given from Standard Input in the following format:


N H
A_1 B_1 C_1 D_1
A_2 B_2 C_2 D_2
:
A_N B_N C_N D_N


Output

If it is possible to arrange the pieces under the conditions, print `YES`; if it is impossible, print `NO`.

Examples

Input

3 4
1 1 0 0
2 2 0 1
3 3 1 0


Output

YES


Input

4 2
1 1 0 1
1 1 0 1
1 1 0 1
1 1 0 1


Output

NO


Input

10 4
1 1 0 3
2 3 2 0
1 2 3 0
2 1 0 0
3 2 0 2
1 1 3 0
3 2 0 0
1 3 2 0
1 1 1 3
2 3 0 0


Output

YES
#include <cstdio>
#include <cstring>
using namespace std;
#define S 200001
int deg[200007], vis[200007], Fa[200007];
inline int Find(register int o){//fprintf(stderr, "%d\n", o);
	return o == Fa[o] ? o : (Fa[o] = Find(Fa[o]));
}
int fastin(){
	register int i; register char ch;
	while (ch = getchar(), ch < '0' || ch > '9');
	i = ch - '0';
	while (ch = getchar(), ch >= '0' && ch <= '9') i = i * 10 + ch - '0';
	return i;
}
int main(){
	register int T, n, h, h2, i, a, b, c, d, u, v;
	T = 1;
	while (T--) {
		n = fastin(), h = fastin();
		memset(deg + 1, 0, sizeof(int) * (h << 1));
		memset(vis + 1, 0, sizeof(int) * (h << 1));
		h2 = h << 1;
		for (i = 1; i <= h2; ++i) Fa[i] = i;
		Fa[S] = S;
		for (i = 1; i <= n; ++i) {
			a = fastin(), b = fastin(), c = fastin(), d = fastin();
			u = (d ? d + h : b);
			v = (c ? c : a + h);
			++deg[u], vis[u] = 1;
			--deg[v], vis[v] = 1;
			Fa[Find(u)] = Find(v);
		}
		//for (i = 1; i <= h2; ++i) fprintf(stderr, "%d %d\n", deg[i], vis[i]);
		//fprintf(stderr, "GG");
		for (i = 1; i <= h; ++i) {
			if (vis[i]) {
				if (deg[i] < 0) break;
				if (deg[i] > 0) Fa[Find(i)] = S;
			}
		}
		if (i <= h) {
			puts("NO");
			continue;
		}
		//fprintf(stderr, "HH");
		for (i = h + 1; i <= h2; ++i) {
			if (vis[i]) {
				if (deg[i] > 0) break;
				if (deg[i] < 0) Fa[Find(i)] = S;
			}
		}
		if (i <= h2) {
			puts("NO");
			continue;
		}
		//fprintf(stderr, "II");
		for (i = 1; i <= h2; ++i) if (vis[i] && Find(i) != S) break;
		//fprintf(stderr, "%d\n", i);
		if (i <= h2) puts("NO");
		else puts("YES");
	}
	return 0;
}