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>
using namespace std;
#define N 1116

int n,h,e[N],f[N],g[N];

int get(int x){
	return f[x]==x?x:f[x]=get(f[x]);
}

int read(){
	int x=0,f=1;char ch=getchar();
	for (;!isdigit(ch);ch=getchar()) if (ch=='-') f=-f;
	for (;isdigit(ch);ch=getchar()) x=x*10+ch-'0';
	return x*f;
}
 
int main(){
	n=read();h=read();
	for (int i=0;i<=2*h;i++) f[i]=i;
	for (int i=1;i<=n;i++){
		int a=read(),b=read(),c=read(),d=read();
		int l=(c?-c:a)+h,r=(d?d:-b)+h;
		e[l]++;e[r]--;f[get(l)]=get(r);g[f[r]]=1;
	}
	for (int i=0;i<=h-1;i++)
		if (e[i]>0) {printf("NO\n");return 0;}
	for (int i=h+1;i<=2*h;i++)
		if (e[i]<0) {printf("NO\n");return 0;}
	for (int i=0;i<=2*h;i++)
		if (e[i]) g[get(i)]=0;
	for (int i=0;i<=2*h;i++)
		if (f[i]==i&&g[i]) {printf("NO\n");return 0;};
	printf("YES\n");return 0;
}