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;
inline void read(int &x)
{
	char c=getchar();
	x=0;
	while (c>'9'||c<'0')
		c=getchar();
	while (c>='0'&&c<='9')
	{
		x=x*10+c-'0';
		c=getchar();
	}
}
const int N=10005;
int n,m,fa[N],v[N],f[N],g[N],x,y,a,b,c,d,flag;
inline int gf(int x)
{
	return fa[x]==x?x:fa[x]=gf(fa[x]);
}
int main()
{
	read(n);
	read(m);
	for (int i=1;i<=1000;++i)
		fa[i]=i;
	for (int i=1;i<=n;++i)
	{
		read(a);
		read(b);
		read(c);
		read(d);
		if (c)
			x=500-c;
		else
			x=500+a;
		if (d)
			y=500+d;
		else
			y=500-b;
		fa[gf(x)]=gf(y);
		++f[x];
		--f[y];
		v[x]=1;
	}
	flag=1;
	for (int i=1;i<500;++i)
		if (f[i]>0)
			flag=0;
	for (int i=501;i<=1000;++i)
		if (f[i]<0)
			flag=0;
	for (int i=1;i<=1000;++i)
		v[gf(i)]|=v[i];
	for (int i=1;i<=1000;++i)
		if (f[i])
			g[gf(i)]=1;
	for (int i=1;i<=1000;++i)
		if (fa[i]==i&&!g[i]&&v[i])
			flag=0;
	puts(flag?"YES":"NO");
	return 0;


}