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 <cstring>
#include <algorithm>
#define y1 yy

using namespace std;

namespace SETS {

int fa[405];

void init() {
  for(int i=1;i<=401;i++) fa[i]=i;
}

int find_father(int x) {
  return (fa[x]==x)?x:fa[x]=find_father(fa[x]);
}

bool check(int x,int y) {
  x=find_father(x);y=find_father(y);
  return x==y;
}

void merge(int x,int y) {
  x=find_father(x);y=find_father(y);
  if (x==y) return;
  fa[x]=y;
}

}

inline int id(int x,int y,bool on) {
  int p=(!y)?x:y+200;
  if (on) {
  	if (p<=200) p+=200; else p-=200;
  }
  return p;
}

int d[405];
bool vis[405];

int main() {
  int n,m;
  scanf("%d%d",&n,&m);
  SETS::init();
  for(int i=1;i<=n;i++) {
  	int x1,x2,y1,y2;
  	scanf("%d%d%d%d",&x1,&x2,&y1,&y2);
  	int p=id(x1,y1,0),q=id(x2,y2,1);
  	vis[p]=vis[q]=1;
  	d[p]++;d[q]--;
  	SETS::merge(p,q);
  }
  int s1=0;
  for(int i=1;i<=200;i++)
    if (d[i]>0) {
    	s1+=d[i];
    	SETS::merge(i,401);
	}
	else if (d[i]<0) {
		puts("NO");
		return 0;
	}
  int s2=0;
  for(int i=201;i<=400;i++)
    if (d[i]<0) {
    	s2-=d[i];
    	SETS::merge(i,401);
	}
	else if (d[i]>0) {
		puts("NO");
		return 0;
	}
  for(int i=1;i<=400;i++)
    if (vis[i]&&!SETS::check(i,401)) {
    	puts("NO");
    	return 0;
	}
  puts("YES");
  return 0;
}