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 fo(i,a,b) for(i=a;i<=b;i++)
#define fd(i,a,b) for(i=a;i>=b;i--)
#define min(a,b) (a<b?a:b)
#define max(a,b) (a>b?a:b)
typedef long long ll;
using namespace std;
inline int read(){
	int n=0,f=1;char c;
	for(c=getchar();(c<'0'||c>'9')&&c!='-';c=getchar());
	if (c=='-') c=getchar(),f=-1;
	for(;c>='0'&&c<='9';c=getchar()) n=n*10+c-48;
	return n*f;
}
const int maxn=400+5;
int n,i,h,A,B,C,D,d[maxn],f[maxn];
bool b[maxn],bz[maxn];
int get(int x){return (f[x])?f[x]=get(f[x]):x;}
void hb(int x,int y){
	x=get(x),y=get(y);
	if (x!=y) f[x]=y;
}
int main(){
	n=read(),h=read()+1;	
	for(;n--;){
		A=read(),B=read(),C=read(),D=read();
		int l=(C)?-C:A,r=(D)?D:-B;
		l+=h,r+=h;
		d[l]--,d[r]++; 
		b[l]=b[r]=1,hb(l,r);
	}
	fo(i,1,h-1) if (d[i]<0) return puts("NO"),0;
	fo(i,h+1,h<<1) if (d[i]>0) return puts("NO"),0;
	fo(i,1,h<<1) if (d[i]) bz[get(i)]=1;
	fo(i,1,h<<1) if (b[i]&&!f[i]&&!bz[i]) return puts("NO"),0;
	puts("YES");
}