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 ll long long
using namespace std;
const int N=10200,M=5000;
inline int read(int x=0,bool f=0,char ch=getchar()){
	for(;!isdigit(ch);ch=getchar()) f=ch=='-';
	for(; isdigit(ch);ch=getchar()) x=(x<<3)+(x<<1)+(ch^48);
	return f?-x:x;
}
int n,h;
int f[N],*fa=f+5000,o[N],*outdu=o+M;
int in[N],*indu=in+M,sz[N],*siz=sz+M;
int c[N],*cnt=c+M;
bool v[N],*vis=v+M;
inline int get(int x){
	return fa[x]==x?x:fa[x]=get(fa[x]);
}
int main(){
	n=read(),h=read();
	for(int i=-h;i<=h;++i) fa[i]=i,siz[i]=1;
	for(int i=1;i<=n;++i){
		int a=read(),b=read(),c=read(),d=read();
		int x=c?c:-a,y=d?-d:b;
		indu[y]++; outdu[x]++;
		if(get(x)!=get(y)) fa[fa[x]]=fa[y],siz[fa[y]]+=siz[fa[x]];
		cnt[get(y)]++;
	}
	bool f=0;
	for(int i=1;i<=h;++i) if(outdu[i]>indu[i]) f=1;
	for(int i=-h;i;++i) if(indu[i]>outdu[i]) f=1;
	for(int i=-h;i<=h;++i) if(cnt[get(i)]&&indu[i]!=outdu[i]) vis[get(i)]=true;
	for(int i=-h;i<=h;++i) if(get(i)==i&&!vis[i]&&cnt[i]) f=1;
	puts(f?"NO":"YES");
	return 0;
}