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<cstdio>
#include<cstring>
#include<cmath>
#include<algorithm>
using namespace std;
const int N=1000005;
int n,h,i,j,k,l,ans,A,B,C,D,g[405][405],u[N],p[N],ind[N],outd[N];
bool vis[N],ok[N];
int find(int x)
{
	return p[x]==-1?x:p[x]=find(p[x]);
}
int main()
{
	scanf("%d%d",&n,&h);
	for(i=1;i<=n;++i)
	{
		scanf("%d%d%d%d",&A,&B,&C,&D);
		if(C)
			A=C+h;
		if(D)
			B=D+h;
		g[A][B<=h?B+h:B-h]++;
		vis[A]=vis[B<=h?B+h:B-h]=true;
	}
	for(i=1;i<=2*h;++i)
		for(j=1;j<=2*h;++j)
			ind[j]+=g[i][j],outd[i]+=g[i][j];
	for(i=1;i<=h;++i)
		if(outd[i]<ind[i])
		{
			puts("NO");
			return 0;
		}
	for(i=h+1;i<=2*h;++i)
		if(outd[i]>ind[i])
		{
			puts("NO");
			return 0;
		}
	for(i=1;i<=2*h;++i)
		p[i]=-1;
	for(i=1;i<=2*h;++i)
		for(j=1;j<=2*h;++j)
			if(g[i][j]&&find(i)!=find(j))
				p[find(i)]=find(j);
	for(i=1;i<=2*h;++i)
		if(outd[i]!=ind[i])
			ok[find(i)]=true;
	for(i=1;i<=2*h;++i)
		if(find(i)==i&&!ok[i]&&vis[i])
		{
			puts("NO");
			return 0;
		}
	puts("YES");
	return 0;
}