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<algorithm>
#include<cmath>
#define SF scanf
#define PF printf
#define MAXN 100010
using namespace std;
int fa[MAXN],ind[MAXN],oud[MAXN],v1[MAXN],v2[MAXN];
int n,h;
bool flag[MAXN];
int get_fa(int x){
	if(fa[x]==0)
		return x;
	fa[x]=get_fa(fa[x]);
	return fa[x];	
}
int main(){
	SF("%d%d",&n,&h);
	int x,y,a,b;
	for(int i=1;i<=n;i++){
		SF("%d%d%d%d",&x,&y,&a,&b);
		int u,v;
		if(a==0)
			u=x+200;
		else
			u=a;
		if(b==0)
			v=y;
		else
			v=b+200;
		flag[u]=flag[v]=1;
		oud[u]++;
		ind[v]++;
		if(get_fa(u)!=get_fa(v))
			fa[get_fa(u)]=get_fa(v);
	}
	for(int i=1;i<=400;i++){
		if(ind[i]>oud[i]){
			v1[get_fa(i)]++;
			if(i>200){
				PF("NO");
				return 0;
			}
		}
		if(ind[i]<oud[i]){
			v2[get_fa(i)]++;
			if(i<=200){
				PF("NO");
				return 0;
			}
		}
	}
	for(int i=1;i<=400;i++)
		if(fa[i]==0)
			if(v1[i]==0&&v2[i]==0&&flag[i]){
				PF("NO");	
				return 0;
			}
	PF("YES");
}