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<cstring>
#include<algorithm>
#include<cassert>
using namespace std;
inline int read(){
	int re=0,flag=1;char ch=getchar();
	while(!isdigit(ch)){
		if(ch=='-') flag=-1;
		ch=getchar();
	}
	while(isdigit(ch)) re=(re<<1)+(re<<3)+ch-'0',ch=getchar();
	return re*flag;
}
int n,h,in[1010],f[1010],v[1010],vis[1010];
int find(int x){return ((f[x]==x)?x:(f[x]=find(f[x])));}
int main(){
	n=read();h=read();int i,a,b,c,d,l,r;
	for(i=1;i<=1000;i++) f[i]=i;
	for(i=1;i<=n;i++){
		a=read();b=read();c=read();d=read();
		if(c) l=-c;
		else l=a;
		if(d) r=d;
		else r=-b;
		l+=500;r+=500;
		f[find(l)]=find(r);
		in[l]++;in[r]--;vis[l]=vis[r]=1;
//		cout<<"addedge "<<l<<' '<<r<<' '<<in[l]<<' '<<in[r]<<' '<<find(l)<<' '<<find(r)<<'\n';
	}
	for(i=1;i<500;i++) if(in[i]>0){puts("NO");return 0;}
	for(i=501;i<=1000;i++) if(in[i]<0){puts("NO");return 0;}
	for(i=1;i<=1000;i++) v[i]=(in[i]!=0);
	for(i=1;i<=1000;i++) v[find(i)]|=v[i];
	for(i=1;i<=1000;i++) if(i==find(i)&&vis[i]&&(!v[i])){puts("NO");return 0;}
	puts("YES");
}
