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<algorithm>
#define maxn 100005
#define N 200
using namespace std;
int n,h,indeg[N*2+5],outdeg[N*2+5];
bool vis[N*2+5];
struct node { int v; node *nxt; } edge[maxn],*head[N*2+5],*ncnt;
void addedge(int u,int v)
{
	ncnt++;
	ncnt->v=v,ncnt->nxt=head[u];
	head[u]=ncnt,indeg[v]++,outdeg[u]++;
}
void dfs(int u)
{
	vis[u]=true;
	for(node *p=head[u];p;p=p->nxt)
		if(!vis[p->v]) dfs(p->v);
}
int main()
{
	scanf("%d%d",&n,&h);
	ncnt=&edge[0];
	for(int i=1;i<=n;i++) 
	{
		int a,b,c,d,l,r;
		scanf("%d%d%d%d",&a,&b,&c,&d);
		//printf(" * %d %d %d %d\n",a,b,c,d);
		l=c?(-c):a,r=d?d:(-b);
		//printf(" - %d %d\n",l,r);
		addedge(l+N,r+N);
	}
	for(int i=0;i<N;i++)
		if(indeg[i]<outdeg[i]) { printf("NO\n"); return 0; }
	for(int i=N+1;i<=N*2;i++)
		if(indeg[i]>outdeg[i]) { printf("NO\n"); return 0; }
	for(int i=0;i<=N*2;i++)
		if(outdeg[i]>indeg[i]&&!vis[i]) dfs(i);
	for(int i=0;i<=N*2;i++)
		if((indeg[i]||outdeg[i])&&!vis[i]) { printf("NO\n"); return 0; }
	printf("YES\n");
}