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<bits/stdc++.h>
#define rint register int
using namespace std;
inline int read(){
	int s=0,f=1;char c=getchar();
	while(c<'0'||c>'9'){if(c=='-')f=0;c=getchar();}
	while(c>='0'&&c<='9')s=(s<<1)+(s<<3)+c-48,c=getchar();
	return f?s:-s;
}
int n,h,ind[410],outd[410];
int fa[410],vis[410];
int get_fa(int x){
	return fa[x]==x?x:fa[x]=get_fa(fa[x]);
}
int main(){
//	freopen("jigsaw.in","r",stdin);
//	freopen("jigsaw.out","w",stdout);
	n=read(); h=read();
	for(rint i=1;i<=h+h;++i) fa[i]=i;
	for(rint i=1;i<=n;++i){
		int a=read(),b=read(),c=read(),d=read();
		int x=c>0?c:-a,y=d>0?-d:b;
		x+=h; y+=h;
		if(get_fa(x)!=get_fa(y)) fa[get_fa(x)]=get_fa(y);
		++ind[y]; ++outd[x];
	}
	for(rint i=-h;i<0;++i)
		if(ind[i+h]>outd[i+h]){
			printf("NO\n");
			return 0;
		}
	for(rint i=1;i<=h;++i)
		if(ind[i+h]<outd[i+h]){
			printf("NO\n");
			return 0;
		}
	for(rint i=0;i<=h+h;++i)
		if(ind[i]!=outd[i]) vis[get_fa(i)]=true;
    for(rint i=0;i<=h+h;++i) 
		if(ind[i]&&outd[i]&&!vis[get_fa(i)]){
			printf("NO\n");
			return 0;
		}
	printf("YES\n");
	return 0;
}