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.



<image>

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<bits/stdc++.h>
#define N 300050
using namespace std;
int n,h;
struct node{
	int a,b,c,d;
}q[N];
int ld[233],lu[233],rd[233],ru[233],ds;
int ind[N],outd[N],fa[N],pd[N];
int getfa(int x){return fa[x]==x?x:fa[x]=getfa(fa[x]);}
int main(){
	cin>>n>>h;
	for(int i=1;i<=n;++i)
		scanf("%d%d%d%d",&q[i].a,&q[i].b,&q[i].c,&q[i].d);
	for(int i=1;i<=h;++i)ld[i]=++ds,fa[ds]=ds;
	for(int i=1;i<=h;++i)lu[i]=++ds,fa[ds]=ds;
	for(int i=1;i<=h;++i)rd[i]=lu[i];
	for(int i=1;i<=h;++i)ru[i]=ld[i];
	for(int i=1;i<=n;++i){
		int pol,por;
		if(q[i].c)pol=ld[q[i].c];
		else pol=lu[q[i].a];
		if(q[i].d)por=rd[q[i].d];
		else por=ru[q[i].b];
		++outd[pol];++ind[por];
		fa[getfa(pol)]=getfa(por);
	}
	int al=0;
	for(int i=lu[1];i<=lu[h];++i){
		al+=outd[i]-ind[i];
		if(outd[i]<ind[i])return puts("NO"),0;
	}
	if(al<=0)return puts("NO"),0;
	for(int i=ru[1];i<=ru[h];++i){
		if(outd[i]>ind[i])return puts("NO"),0;
		al+=outd[i]-ind[i];
	}
	if(al)return puts("NO"),0;
	for(int i=1;i<=ds;++i)if(ind[i]!=outd[i])pd[getfa(i)]=1;
	for(int i=1;i<=ds;++i)if((ind[i]||outd[i])&&!pd[getfa(i)])return puts("NO"),0;
	return puts("YES"),0;
}