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<cstdio>
#include<cstring>
#include<algorithm>
#define fo(i,a,b) for(int i=a;i<=b;i++)
#define N 101000
#define M 510
using namespace std;
int last[M],nxt[N],n,m,to[N],rd[M],cd[M],tot=0,bz[M];
void link(int x,int y)
{
	nxt[++tot]=last[x];last[x]=tot;to[tot]=y;
	rd[y]++;cd[x]++;
}
void dg(int x)
{
	if(bz[x]==1) return;bz[x]=1;
	for(int i=last[x];i;i=nxt[i]) dg(to[i]);
}
int main()
{
	scanf("%d%d",&n,&m);
	fo(i,1,n)
	{
		int a,b,c,d,x,y;scanf("%d%d%d%d",&a,&b,&c,&d);
		if(c==0) x=a+m;
		else x=c;
		if(d==0) y=b;
		else y=d+m;
		link(x,y);
	}
	int q=0,w=0;
	fo(i,1,m)
	{
		if(rd[i]<cd[i]) q++;
		if(rd[i]>cd[i]) w++;
	}
	if(q>0||w==0) return printf("NO\n"),0;
	q=0,w=0;
	fo(i,m+1,m+m)
	{
		if(rd[i]>cd[i]) q++;
		if(rd[i]<cd[i]) w++;
	}
	if(q>0||w==0) return printf("NO\n"),0;
	q=0,w=0;
	fo(i,1,m) if(rd[i]>cd[i]) w++;
	fo(i,m+1,m+m) if(rd[i]<cd[i]) q++;
//	if(q!=w) return printf("NO\n"),0;
	fo(i,m+1,m+m) if(rd[i]<cd[i]) dg(i);
	fo(i,1,m) if((rd[i]>0||cd[i]>0)&&bz[i]==0) return printf("NO\n"),0;
	printf("YES\n");
}