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<algorithm>
#include<cstring>
#include<cmath>
using namespace std;
#define fo(i,j,k) for(i=j;i<=k;i++)
#define fd(i,j,k) for(i=j;i>=k;i--)
#define cmax(a,b) (a=(a>b)?a:b)
#define cmin(a,b) (a=(a<b)?a:b)
typedef long long ll;
const int N=1e6+5,M=2e6+5,mo=998244353;
int fa[N],n,H,A,B,C,D,i,pp,pd[N],chu[N],ru[N],l,r,act[N];
int get(int x)
{
	if (fa[x]==x) return x;
	return fa[x]=get(fa[x]);
}
int main()
{
	scanf("%d %d\n",&n,&H);
	fo(i,0,H*2) fa[i]=i;
	fo(i,1,n)
	{
		scanf("%d %d %d %d",&A,&B,&C,&D);
		if (!C) l=A;else l=-C; 
		if (!D) r=-B;else r=D;
		l+=H;
		r+=H;
		//e=(l,r)
		act[l]=act[r]=1;
		chu[l]++;
		ru[r]++;
		fa[get(l)]=get(r);
	}
	pp=1;
	// neg: in>=out
	fo(i,0,H) if (ru[i]<chu[i]) pp=0;
	// pos: in<=out
	fo(i,H+1,2*H) if (ru[i]>chu[i]) pp=0;
	fo(i,0,2*H) pd[get(i)]|=(ru[i]!=chu[i]);
	pd[H]=1;
	fo(i,0,2*H) if (act[i]&&!pd[get(i)]) pp=0;
	if (pp) printf("YES");else
	printf("NO");
}