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<cstring>
#include<algorithm>
#define MAXN 100000
#define MAXH 400
using namespace std;
int N,H;
int setfa[MAXH+5],cd[MAXH+5],rd[MAXH+5];
int A[MAXN+5],B[MAXN+5],C[MAXN+5],D[MAXN+5];
int ok[MAXH+5];
void Init()
{
	for(int i=1;i<=MAXH;i++)
		setfa[i]=i;
}
int Findfa(int x)
{
	if(x==setfa[x])
		return x;
	return setfa[x]=Findfa(setfa[x]);
}
void Union(int x,int y)
{
	int fx=Findfa(x),fy=Findfa(y);
	if(fx==fy)
		return;
	setfa[fx]=fy;
}
int main()
{
	Init();
	scanf("%d %d",&N,&H);
	for(int i=1;i<=N;i++)
	{
		scanf("%d %d %d %d",&A[i],&B[i],&C[i],&D[i]);
		int x,y;
		if(C[i]==0)	x=A[i];
		else		x=C[i]+H;
		if(D[i]==0)	y=B[i]+H;
		else		y=D[i];
		cd[x]++,rd[y]++;
		Union(x,y);
	}
	bool legal=true;
	for(int i=1;i<=MAXH;i++)
	{
		int fi=Findfa(i);
		if(cd[fi]==0&&rd[fi]==0)
			continue;
		if(cd[i]!=rd[i])
		{
			if(cd[i]>rd[i]&&i>H)
				legal=false;
			else if(cd[i]<rd[i]&&i<=H)
				legal=false;
			ok[fi]=1;
		}
	}
	for(int i=1;i<=MAXH;i++)
	{
		int fi=Findfa(i);
		if(cd[fi]!=0||rd[fi]!=0)
			if(ok[fi]==false)
			{
				legal=false;
				break;
			}
	}
	if(legal==true)
		printf("YES\n");
	else
		printf("NO\n");
	return 0;
}