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<cstdlib>
#include<ctime>
#include<utility>
#include<cmath>
#include<functional>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
void sort(int &a,int &b)
{
	if(a>b)
		swap(a,b);
}
void open(const char *s)
{
#ifndef ONLINE_JUDGE
	char str[100];
	sprintf(str,"%s.in",s);
	freopen(str,"r",stdin);
	sprintf(str,"%s.out",s);
	freopen(str,"w",stdout);
#endif
}
int rd()
{
	int s=0,c;
	while((c=getchar())<'0'||c>'9');
	do
	{
		s=s*10+c-'0';
	}
	while((c=getchar())>='0'&&c<='9');
	return s;
}
int upmin(int &a,int b)
{
	if(b<a)
	{
		a=b;
		return 1;
	}
	return 0;
}
int upmax(int &a,int b)
{
	if(b>a)
	{
		a=b;
		return 1;
	}
	return 0;
}
int f[810];
int v[810];
int e[810];
int deg[810];
int find(int x)
{
	return f[x]==x?x:f[x]=find(f[x]);
}
int main()
{
	int n,h;
	scanf("%d%d",&n,&h);
	int i;
	for(i=1;i<=800;i++)
		f[i]=i;
	int a,b,c,d,l,r;
	for(i=1;i<=n;i++)
	{
		scanf("%d%d%d%d",&a,&b,&c,&d);
		if(c)
			l=-c;
		else
			l=a;
		if(d)
			r=d;
		else
			r=-b;
		l+=400;
		r+=400;
		deg[l]++;
		deg[r]--;
		v[l]=v[r]=1;
		f[find(r)]=find(l);
	}
	for(i=1;i<=400;i++)
		if(deg[i]>0)
		{
			printf("NO\n");
			return 0;
		}
	for(i=401;i<=800;i++)
		if(deg[i]<0)
		{
			printf("NO\n");
			return 0;
		}
	for(i=1;i<=800;i++)
		if(deg[i])
			e[find(i)]=1;
	for(i=1;i<=800;i++)
		v[find(i)]|=v[i];
	for(i=1;i<=800;i++)
		if(i==find(i)&&v[i]&&!e[i])
		{
			printf("NO\n");
			return 0;
		}
	printf("YES\n");
	return 0;
}