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 <iostream>
#include <cstdio>
#include <cctype>

using namespace std;

inline int read()
{
	int x=0,f=1;
	char ch=getchar();
	while (!isdigit(ch)) f=ch=='-'?-1:f,ch=getchar();
	while (isdigit(ch)) x=x*10+ch-'0',ch=getchar();
	return x*f;
}

const int MAXH=200;
const int V=(MAXH<<1)+5;

int fa[V],deg[V]/*in - out*/,size[V];
bool sat[V];
int n,H;

int getfather(int son){return fa[son]==son?son:fa[son]=getfather(fa[son]);}

inline void addedge(int x,int y)
{
	--deg[x],++deg[y];
	int fx=getfather(x),fy=getfather(y);
	if (!size[fx]) size[fx]=1;
	if (!size[fy]) size[fy]=1;
	if (fx!=fy) fa[fy]=fx,size[fx]+=size[fy];
}

int main()
{
	//freopen("jigsaw.in","r",stdin),freopen("jigsaw.out","w",stdout);
	n=read(),H=read();
	for (int i=0;i<=H<<1;++i) fa[i]=i;
	for (int i=1,a,b,c,d;i<=n;++i)
	{
		a=read(),b=read(),c=read(),d=read();
		int l=(c?-c:a)+H,r=(d?d:-b)+H;
		addedge(l,r);
	}
	bool judge=1;
	for (int x=0;judge&&x<=H<<1;++x)
		if (x-H)
		{
			if (x-H<0) judge&=deg[x]>=0;
			else judge&=deg[x]<=0;
			sat[getfather(x)]|=deg[x];
		}
	for (int x=0;judge&&x<=H<<1;++x) if (x==getfather(x)&&size[x]) judge&=sat[x];
	printf(judge?"YES\n":"NO\n");
	//fclose(stdin),fclose(stdout);
	return 0;
}