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<queue>
#include<ctime>
#include<vector>
#include<cstdio>
#include<cmath>
#include<cstring>
#include<string>
#include<memory.h>
#include<map>
#include<ctime>
#include<algorithm>
#include<ctime>
#define ll int
#define For(i,j,k)  for(ll i=j;i<=k;++i)
#define FOr(i,j,k)  for(ll i=j;i>=k;--i)
#define ld double
using namespace std;
inline ll read(){   ll x=0,f=1;char ch=getchar();   while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}  while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}  return x*f; }
inline void wrote(ll x){    if (x<0) putchar('-'),x=-x; if (x>=10) wrote(x/10);   putchar(x%10+'0');  }
inline void writeln(ll x){ wrote(x);   puts("");   }
const ll N=1010;
ll n,h,ans,fa[N],C[N],D[N],vis[N];
ll find(ll x){	return x==fa[x]?x:fa[x]=find(fa[x]);	}
int main(){
	n=read();	read();
	For(i,1,1000)	fa[i]=i;
	For(i,1,n){
		ll a=read(),b=read(),c=read(),d=read();
		a=c?-c:a;	b=d?d:-b;	a+=500;	b+=500;
		fa[find(a)]=find(b);
		D[a]++;	D[b]--;	vis[a]=1;
	}
	bool fl=1;
	For(i,1,499)	fl&=D[i]<=0;
	For(i,501,1000)	fl&=D[i]>=0;
	For(i,1,1000)	vis[find(i)]|=vis[i];
	For(i,1,1000)	if (D[i])	C[find(i)]=1;
	For(i,1,1000)	fl&=(fa[i]!=i)||C[i]||!vis[i];
	puts(fl?"YES":"NO");
}