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.



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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 <bits/stdc++.h>

using namespace std;

const int maxn = 100010;
const int maxh = 210;

int n, h, e, f;
int l[maxh<<1], in_deg[maxh<<1], out_deg[maxh<<1], vis[maxh<<1];

struct Edge {
	int v, x;
} E[(maxn<<1)+(maxh<<2)];

inline void addEdge(int u, int v) {
	E[e].v = v, E[e].x = l[u], l[u] = e++;
}

void dfs(int u) {
	vis[u] = 1;
	if (in_deg[u] != out_deg[u]) f = 1;
	for (int p = l[u]; p >= 0; p = E[p].x) {
		int v = E[p].v;
		if (!vis[v]) dfs(v);
	}
}

int main() {
	memset(l, -1, sizeof(l));
	scanf("%d%d", &n, &h);
	for (int i = 1; i <= n; i++) {
		int a, b, c, d; scanf("%d%d%d%d", &a, &b, &c, &d);
		int u, v;
		if (c) u = c+h;
		else u = a;
		if (d) v = d;
		else v = b+h;
		addEdge(u, v), addEdge(v, u);
		++ in_deg[v], ++ out_deg[u];
	}
	int ok = 1;
	for (int i = 1; i <= h; i++) {
		if (in_deg[i] > out_deg[i]) ok = 0;
		if (in_deg[i+h] < out_deg[i+h]) ok = 0;
	}
	for (int i = 1; i <= 2*h; i++) {
		if ((in_deg[i] || out_deg[i]) && !vis[i]) {
			f = 0;
			dfs(i);
			if (!f) ok = 0;
		}
	}
	if (ok) puts("YES");
	else puts("NO");
	return 0;
}