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 <cstdio>
#include <cstdlib>
#include <iostream>
#include <cmath>
#include <algorithm>
#include <cstring>
#define fo(i,a,b) for(int i=a;i<=b;i++)
#define fod(i,a,b) for(int i=a;i>=b;i--)
#define N 100005
#define M 405
using namespace std;
bool bz[N];
int cd[M],rd[M],n,num,f[M],h,m,v1[M],v2[M];
int getf(int k)
{
	if(f[k]==k||!f[k]) return k;
	return (f[k]=getf(f[k]));
}
int main()
{
	cin>>n>>h;
	fo(i,1,n)
	{
		int a,b,c,d,x,y;
		scanf("%d%d%d%d",&a,&b,&c,&d);
		x=(c>0)?c:(a+200);
		y=(d>0)?(d+200):b;
		cd[x]++,rd[y]++;
		int fx=getf(x),fy=getf(y);
		f[fx]=fy;
	}
	int w=0;
		bool pd=1;
		fo(i,1,400) 
		{
			if(rd[i]>0||cd[i]>0)
			{
				int fa=getf(i);
				if(rd[i]-cd[i]<0) 
				{
					v1[fa]++;
					if(i<=200)
					{
						pd=0;
						break;
					}
				}
				if(rd[i]-cd[i]>0) 
				{
					v2[fa]++;
					if(i>200)
					{
						pd=0;
						break;
					}
				}
			}
		}
		if(pd)
		fo(i,1,400)
		{
			if((rd[i]||cd[i])&&v1[getf(i)]==0) 
			{
				pd=0;
				break;
			}
		}
		if(pd) printf("YES\n");
		else printf("NO\n"); 
}