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 re register
#define inc(i,j,k) for(re int i=j;i<=k;i++)
using namespace std;
const int N=405;
inline int read(){
	int x=0;
	char ch=getchar();
	while(ch<'0'||ch>'9') ch=getchar();
	while('0'<=ch&&ch<='9') x=x*10+ch-'0',ch=getchar();
	return x;
}
int n,h,fa[N],in[N],ot[N];
bool flag[N];
int gf(int x){return fa[x]==x?x:fa[x]=gf(fa[x]);}
int main(){
	n=read(),h=read()*2;
	inc(i,1,h) fa[i]=i; 
	inc(i,1,n){
		int a=read(),b=read(),c=read(),d=read();
		int l=c?c+(h>>1):a,r=d?d:b+(h>>1);
		ot[l]++,in[r]++;
		l=gf(l),r=gf(r);
		if(l!=r) fa[l]=r;
	}
	inc(i,1,(h>>1)) if(in[i]>ot[i]) return puts("NO"),0;
	inc(i,(h>>1)+1,h) if(ot[i]>in[i]) return puts("NO"),0;
	inc(i,1,h) if(in[i]!=ot[i]||!in[i]&&!ot[i]) flag[gf(i)]=1;
	inc(i,1,h) if(fa[i]==i&&!flag[i]) return puts("NO"),0;
	puts("YES");
}