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>
using namespace std;
const int maxn=405,maxm=100500;
inline int read(int x=0,char c=getchar()){for(;c>'9'||c<'0';c=getchar());for(;c>='0'&&c<='9';c=getchar()) x=x*10+c-48;return x;}
int fa[maxn];
bool v[maxn];
int in[maxn],out[maxn],A[maxm],B[maxm],C[maxm],D[maxm],pa[maxm];
int find(int x){return fa[x]==x?x:fa[x]=find(fa[x]);}
int main(){
	int n,h,tot=0;cin>>n>>h;bool flag=1;
	for(int i=1;i<=n;++i) A[i]=read(),B[i]=read(),C[i]=read(),D[i]=read();//h<<=1;
	for(int i=1;i<=n;++i) {
		int a,b;
		if(!C[i]) a=h+A[i];else a=h-C[i];
		if(!D[i]) b=h-B[i];else b=h+D[i];
		++out[a],++in[b];
	}
	for(int i=0;i<h;++i) if(in[i]<out[i]) flag=0;//cout<<flag<<endl;
	for(int i=h+1;i<=h<<1;++i) if(in[i]>out[i]) flag=0;
	for(int i=0;i<=h<<1;++i) fa[i]=i,v[i]=(in[i]!=out[i]);
	for(int i=1;i<=n;++i){
		int a,b;
		if(!C[i]) a=h+A[i];else a=h-C[i];
		if(!D[i]) b=h-B[i];else b=h+D[i];
		if(find(a)==find(b)) pa[++tot]=a;
		else v[find(b)]|=v[find(a)],fa[find(a)]=find(b);
	}
	for(int i=1;i<=tot;++i) if(!v[find(pa[i])]) flag=0;
	puts(flag?"YES":"NO");
	return 0;
}