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<cstdlib>
#include<cstring>
#include<algorithm>
#define fo(i,j,k) for(int i=j;i<=k;++i)
#define fd(i,j,k) for(int i=j;i>=k;--i)
#define rep(i,x) for(int i=ls[x];i;i=nx[i])
using namespace std;
const int N=420,M=1e5+10;
int to[M],nx[M],ls[N],vl[M],num=0;
int rd[N],cd[N];
bool cz[N],vis[N];;
void link(int u,int v){
	cz[u]=cz[v]=1;
	to[++num]=v,nx[num]=ls[u],ls[u]=num;
}
void dfs(int x){
	if(vis[x]) return;
	vis[x]=1;
	rep(i,x) dfs(to[i]);
}
int main()
{
	int n,h;
	scanf("%d %d",&n,&h);
	fo(i,1,n){
		int a,b,c,d,u,v;
		scanf("%d %d %d %d",&a,&b,&c,&d);
		u=c?c:a+h,v=d?d+h:b;
		link(u,v),cd[u]++,rd[v]++;
	}
	bool tf=false;
	fo(i,1,h) if(cz[i]){
		if(rd[i]<cd[i]) return printf("NO"),0;
		tf|=rd[i]>cd[i];
	}
	if(!tf) return printf("NO"),0;
	tf=false;
	fo(i,h+1,h<<1) if(cz[i]){
		if(rd[i]>cd[i]) return printf("NO"),0;
		tf|=rd[i]<cd[i];
	}
	if(!tf) return printf("NO"),0;
	fo(i,h+1,h<<1) if(cz[i] && rd[i]<cd[i]) dfs(i);
	fo(i,1,h) if(cz[i] && !vis[i]) return printf("NO"),0;
	printf("YES");
}
