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>
#define L long long
#define vi vector<int>
#define pb push_back
#define pi pair<int,int>
#define pii pair<pi,int>
#define aa first
#define bb second
#define xx aa.aa
#define yy aa.bb
#define zz bb
#define mp make_pair
#define mpp(a,b,c) mp(mp(a,b),c)
using namespace std;
int n,m,a,b,c,d,w[410],f[410],u[410];
inline int fa(int i)
{
	return i==f[i]?i:f[i]=fa(f[i]);
}
int main()
{
	//freopen("b102.txt","r",stdin);
	//freopen("x.out","w",stdout);
	int i,j,k,l;
	scanf("%d%d",&n,&m);
	for(i=1;i<=2*m;i++)
	  f[i]=i;
	for(i=1;i<=n;i++)
	  {
	   scanf("%d%d%d%d",&a,&b,&c,&d);
	   if(c)
	     j=c+m;
	   else
	     j=a;
	   if(d)
	     k=d;
	   else
	     k=b+m;
	   w[j]++;
	   w[k]--;
	   f[fa(j)]=fa(k);
	   u[j]=u[k]=1;
	  }
	for(l=1;l<=2*m;l++)
	{
	for(i=1,j=k=0;i<=2*m;i++)
	  if(fa(i)==l)
	  if(w[i]>0)
	    if(i<=m)
	      j+=w[i];
	    else
	      break;
	  else if(w[i]<0)
	    if(i>m)
	      k+=-w[i];
	    else
	      break;
	if(i<=2*m || j!=k)
	  {
	   printf("NO\n");
	   return 0;
	  }
	if(!j && !k)
	  {
	   for(i=1,j=k=0;i<=2*m;i++)
	     if(fa(i)==l)
	     if(u[i])
	       if(i<=m)
	         j++;
	       else
	         k++;
	   if(j+k)
	     {
	      printf("NO\n");
	      return 0;
		 }
	  }
	}
	printf("YES\n");
	return 0;
}
