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<cstdio>
#include<cstring>
#include<algorithm>
#define fo(i,a,b) for(int i=a;i<=b;i++)
#define fd(i,b,a) for(int i=b;i>=a;i--)
#define mset(a,x) memset(a,x,sizeof(a))
using namespace std;
typedef long long ll;
char ch;
int read(){int n=0,p=1;for(ch=getchar();ch<'0' || '9'<ch;ch=getchar())if(ch=='-') p=-1;for(;'0'<=ch && ch<='9';ch=getchar()) n=n*10+ch-'0';return n*p;}
const int N=1e5+5;
int n,h,cl[N],cr[N],d[N],fa[N];
int getfa(int x){return fa[x]?fa[x]=getfa(fa[x]):x;}
bool bz[N],exi[N];
void link(int u,int v)
{
	--d[u],++d[v];
	int fu=getfa(u),fv=getfa(v);
	if(fu!=fv) fa[fv]=fu;
}
int main()
{
	n=read(),h=read();
	fo(i,1,n)
	{
		int x,y,A=read(),B=read(),C=read(),D=read();
		if(C) x=-C;else x=A;
		if(D) y=D;else y=-B;
		x+=h,y+=h,exi[x]=exi[y]=1;
		link(x,y);
	}
	fo(i,0,h) if(d[i]<0) return puts("NO"),0;
	fo(i,h+1,h+h) if(d[i]>0) return puts("NO"),0;
	fo(i,0,h+h) if(d[i]) bz[i]=1;
	fo(i,0,h+h) bz[getfa(i)]|=bz[i];
	fo(i,0,h+h)
		if(i==getfa(i) && exi[i] && !bz[i]) return puts("NO"),0;
	return puts("YES"),0;
}