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;
int fa[1010],num[1010];
bool go[1010],bo[1010];
int getf(int s){if (fa[s]==s) return s;return fa[s]=getf(fa[s]);}
int main()
{
	int n;scanf("%d%*d",&n);
	for (int i=1;i<=1000;i++) fa[i]=i;
	for (int i=1;i<=n;i++)
	{
		int a,b,c,d;scanf("%d%d%d%d",&a,&b,&c,&d);
		if (c==0) c=a+500;else c=500-c;
		if (d==0) d=500-b;else d=d+500;
		fa[getf(c)]=getf(d);
		num[c]++;num[d]--;bo[c]=true;
	}
	for (int i=1;i<500;i++) if (num[i]>0) {puts("NO");return 0;}
	for (int i=501;i<1000;i++) if (num[i]<0) {puts("NO");return 0;}
	for (int i=1;i<1000;i++)
	{
		bo[getf(i)]|=bo[i];
		go[getf(i)]|=(num[i]!=0);
	}
	for (int i=1;i<1000;i++) if ((fa[i]==i)&&(bo[i])&&(!go[i])) {puts("NO");return 0;}
	puts("YES");
}