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 <iostream>
#include <cstdio>
#include <cstring>
using namespace std;
struct P{
	int a,b,c,d;
}a[100005];
struct edge{
	int k,next;
}e[200005];
int n,h,IN[405],home[405],cnt=-1;
void add(int x,int y){
	cnt++;
	e[cnt].k=y;
	e[cnt].next=home[x];
	home[x]=cnt;
}
int D;
bool vis[405],used[405];
void dfs(int k){
	vis[k]=1;
	if(IN[k]) D=1;
	for(int i=home[k];~i;i=e[i].next) if(!vis[e[i].k])
		dfs(e[i].k);
}
int main(){
	memset(home,-1,sizeof(home));
	scanf("%d%d",&n,&h);
	for(int i=1;i<=n;i++){
		scanf("%d%d%d%d",&a[i].a,&a[i].b,&a[i].c,&a[i].d);
		int x=a[i].c?a[i].c:a[i].a+h,y=a[i].d?a[i].d+h:a[i].b;
		add(x,y);add(y,x);
		IN[x]--;IN[y]++;
	}
	int t=0;
	for(int i=1;i<=h;i++) if(IN[i]<0) t=1;
	for(int i=h+1;i<=h+h;i++) if(IN[i]>0) t=1;
	if(t) return puts("NO"),0;
	for(int i=1;i<=h+h;i++) if(!vis[i]&&home[i]!=-1){
		D=0;dfs(i);
		if(!D) return puts("NO"),0;
	}
	puts("YES");
	return 0;
}