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<bits/stdc++.h>
#define ll long long
using namespace std;
int n,h;
tuple<int,int,int,int> a[100010];int fa[100010];
int find(const int &x){return fa[x]==x?x:fa[x]=find(fa[x]);}
int ii[100010],oo[100010],mapp[100010];
void init(){
	for(int i=1;i<=n;i++){
		int f,t;
		if(f=get<2>(a[i])) f+=h;
		else f=get<0>(a[i]);
		if(t=get<3>(a[i]));
		else t=get<1>(a[i])+h;
		oo[f]++,ii[t]++;f=find(f),t=find(t);
		if(f^t) fa[f]=t;
	}
}
int main(){
	scanf("%d%d",&n,&h);
	for(int i=1;i<=1000;i++) fa[i]=i;
	int A,B,C,D;
	for(int i=1;i<=n;i++) scanf("%d%d%d%d",&A,&B,&C,&D),a[i]={A,B,C,D};
	bool fg=1;init();
	for(int i=1;i<=h;i++) if(ii[i]>oo[i]) fg=0;
	for(int i=h+1;i<=h+h;i++) if(ii[i]<oo[i]) fg=0;
	for(int i=1;i<=h+h;i++) if(ii[i]!=oo[i]||(ii[i]+oo[i]==0)) mapp[find(i)]++;
	for(int i=1;i<=h+h;i++) if(!mapp[i]&&i==fa[i]) fg=0;
	printf("%s\n",fg?"YES":"NO");
}
