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>
#define retrun return
#define cpnst const
int CT[444][444],DEG[444],SZ[444],Lm=401;
class UFS
{
	int Fa[1111];
	public:
	void init(){for(register int i=1;i<=1000;i++)Fa[i]=i;}
	int rt(int x){return Fa[x]^x?Fa[x]=rt(Fa[x]):x;}
	bool merge(int x,int y){return x=rt(x),y=rt(y),Fa[x]=y,x^y;}
}U;
void rd()
{
	int a,b,c,d;
	scanf("%d%d%d%d",&a,&b,&c,&d);
	if(c)a=-c;if(d)b=d;else b=-b;
	U.merge(a+201,b+201),CT[a+201][b+201]++,
	DEG[a+201]++,DEG[b+201]--,SZ[a+201]++,SZ[b+201]++;
}
int UNB[11111];
void cover(int x)
{UNB[U.rt(x)]=1;}
int main()
{
	register int i;
	int n;
	scanf("%d%*d",&n),U.init();
	for(i=1;i<=n;i++)rd();
	for(i=-200;i<=200;i++)
	{
		if(i<0&&DEG[i+201]>0)return puts("NO"),0;
		if(i>0&&DEG[i+201]<0)return puts("NO"),0;
	}for(i=1;i<=Lm;i++)
		if(DEG[i])cover(i);
	for(i=1;i<=Lm;i++)
		if(SZ[i])
			if(!UNB[U.rt(i)])return puts("NO"),0;
	puts("YES");
}
/*
Just go for it.
*/