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>
#define maxn 405
#define o 203
using namespace std;

int n,H,in[maxn];
int F[maxn],hd[maxn],sz[maxn];
int Find(int u){ return !F[u] ? u : F[u] = Find(F[u]); }

int main(){
	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 x , y;
		if(C == 0) x = A;
		else x = - C;
		if(D == 0) y = -B;
		else y = D;
		x += o , y += o;
		in[y] ++ ,in[x] --;
		if(Find(x) != Find(y))
			F[Find(x)] = Find(y);
		sz[Find(y)] = 2; 
	}
	bool ER = 0;
	for(int i=1;i<maxn;i++){
		if(i < o && in[i] < 0) ER = 1;
		if(i > o && in[i] > 0) ER = 1;
		if(i > o && in[i] < 0) hd[Find(i)] = 1;
	}
	for(int i=1;i<maxn;i++) if(Find(i) == i && sz[i] > 1 && !hd[i])
		ER = 1;
	if(ER) puts("NO");
	else puts("YES");
}