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<iostream>
#define neko 100010
#define heko 410
#define qwq return printf("YES"),0; 
#define orz return printf("NO"),0; 
#define f(i,a,b) for(register int i=(a);i<=(b);i=-(~i))
static int n,H;
typedef int arr[heko];
arr fa,book,dgi,dgo,out;
namespace IO
{
	const unsigned int bufsize=1<<16,outsize=1<<24;
	static char ch[bufsize],*S=ch,*T=ch;
	inline char getc()
	{return ((S==T)&&(T=(S=ch)+fread(ch,1,bufsize,stdin),S==T)?0:*S++);}
	static char Out[outsize],*nowp=Out;
	inline void flush(){fwrite(Out,1,nowp-Out,stdout);nowp=Out;}
	template<typename T>
		void read(T &x)
		{
			char c=getc();x=0;
			for(;!isdigit(c);c=getc());
			for(;isdigit(c);x=(x<<1)+(x<<3)+(c^'0'),c=getc());
		}
	template<typename T>
		void write(T x,char c='\n')
		{
			if(!x)*nowp++='0';
			static unsigned int stk[50],tp=0;
			for(;x;x/=10)stk[++tp]=x%10;
			for(;tp;*nowp++=stk[tp--]^'0');*nowp++=c;
		}
}
int find(int x){return fa[x]^x?fa[x]=find(fa[x]):x;}
int main()
{
	using namespace IO;
	int x,y,z,o,X,Y;
	read(n),read(H);
	f(i,0,H<<1)fa[i]=i;
	f(i,1,n)
	{
		read(x),read(y),read(z),read(o);
		if(z==0)X=H+x;
		else X=H-z;
		if(o==0)Y=H-y;
		else Y=H+o;
		book[X]=book[Y]=1;
		++dgi[Y],++dgo[X];
		fa[find(Y)]=find(X);

	}
	f(i,0,H)if(dgi[i]<dgo[i])orz;
	f(i,H+1,H<<1)if(dgi[i]>dgo[i])orz;
	f(i,0,H<<1)if(dgi[i]^dgo[i])out[fa[i]]=1;
	f(i,0,H<<1)if(fa[i]==i&&book[i]&&!out[fa[i]])orz;
	qwq;
}