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 <cstdio>
#include <algorithm>
using namespace std;

const int MAXH = 400;

int fa[MAXH + 5], ind[MAXH + 5], oud[MAXH + 5], N, H;
int find(int x) {return fa[x] = ((fa[x] == x) ? x : find(fa[x]));}
void unite(int u, int v) {
	int fu = find(u), fv = find(v);
	if( fu != fv ) fa[fu] = fv;
}
void adde(int u, int v) {ind[v + H]++, oud[u + H]++, unite(u + H, v + H);}

int a[MAXH + 5], b[MAXH + 5];
int main() {
	scanf("%d%d", &N, &H);
	for(int i=0;i<=2*H;i++) fa[i] = i;
	for(int i=1,A,B,C,D;i<=N;i++) {
		scanf("%d%d%d%d", &A, &B, &C, &D), D = -D;
		if( !C ) C = -A; if( !D ) D = B;
		adde(C, D);
	}
//	for(int i=0;i<=2*H;i++) printf("%d %d\n", ind[i], oud[i]);
	
	int deg = 0;
	for(int i=0;i<H;i++) {
		if( ind[i] > oud[i] ) {
			puts("NO");
			return 0;
		} else a[find(i)] += (oud[i] - ind[i]), deg += (oud[i] - ind[i]);
	}
	for(int i=H+1;i<=2*H;i++) {
		if( oud[i] > ind[i] ) {
			puts("NO");
			return 0;
		} else b[find(i)] += (ind[i] - oud[i]), deg += (oud[i] - ind[i]);
	}
	if( deg ) {
		puts("NO");
		return 0;
	}
	for(int i=0;i<=2*H;i++) {
		if( !ind[i] || !oud[i] ) continue;
		if( find(i) == i && (!a[i] || !b[i]) ) {
			puts("NO");
			return 0;
		}
	}
	puts("YES");
}