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.



<image>

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>

int head[401],nxt[200001],b[200001],k,n,h,ind[401],outd[401],f[401];
bool vis[401];
void push(int s,int t){
//	printf("push %d %d\n",s,t);
	nxt[++k]=head[s];
	head[s]=k;
	b[k]=t;
	++ind[t];
	++outd[s];
}
int find(int x){return f[x]?f[x]=find(f[x]):x;}
bool check(){
	for(int i=1;i<=h;i++)if(ind[i]>outd[i])return 0;
	for(int i=h+1;i<=(h<<1);i++)if(ind[i]<outd[i])return 0;
	for(int i=1;i<=(h<<1);i++)
		for(int j=head[i];j;j=nxt[j]){
			int u=find(i),v=find(b[j]);
			if(u!=v)f[u]=v;
		}
	for(int i=1;i<=(h<<1);i++)if(ind[i]!=outd[i])vis[find(i)]=1;
	for(int i=1;i<=(h<<1);i++)if(ind[i]&&!vis[find(i)])return 0;
	return 1;
}
int main(){
	scanf("%d%d",&n,&h);
	for(int i=1,a,b,c,d;i<=n;i++)
		scanf("%d%d%d%d",&a,&b,&c,&d),
		push((!c)?a:(h+c),(!d)?h+b:d);
	if(check())puts("YES");
	else puts("NO");
}