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
//Love and Freedom.
#include<cmath>
#include<cstdio>
#include<cstring>
#include<algorithm>
#define ll long long
#define inf 20021225
#define M 510
using namespace std;
int read()
{
	int s=0,f=1; char ch=getchar();
	while(ch<'0'||ch>'9'){if(ch=='-') f=-1; ch=getchar();}
	while(ch>='0'&&ch<='9') s=s*10+ch-'0',ch=getchar();
	return f*s;
}
int in[M],out[M],fa[M],n,h,a,b,c,d; bool vis[M];
int find(int x){return x==fa[x]?x:fa[x]=find(fa[x]);} 
int main()
{
	n=read(),h=read();
	for(int i=0;i<=2*h;i++)	fa[i]=i;
	for(int i=1;i<=n;i++)
	{
		a=read(),b=read(),c=read(),d=read();
		int l=c>0?c:-a,r=d>0?-d:b; l+=h,r+=h;
		if(find(l)!=find(r))	fa[find(l)]=find(r);
		out[l]++; in[r]++;
	}
	for(int i=-h;i<0;i++)	if(in[i+h]>out[i+h])	return puts("NO"),0;
	for(int i=1;i<=h;i++)	if(out[i+h]>in[i+h])	return puts("NO"),0;
	for(int i=0;i<=h*2;i++)	if(in[i]!=out[i])	vis[find(i)]=1;
	for(int i=0;i<=h*2;i++)	if((in[i]||out[i])&&!vis[find(i)])	return puts("NO"),0;
	return puts("YES"),0;
}
