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>
using namespace std;
typedef long long LL;
typedef unsigned long long ULL;
int read(){
	int x=0;
	char ch=getchar();
	while (!isdigit(ch))
		ch=getchar();
	while (isdigit(ch))
		x=(x<<1)+(x<<3)+(ch^48),ch=getchar();
	return x;
}
const int N=405;
int n,m=401;
int fa[N],in[N],out[N],cnt[N],f[N];
int _(int k){
	if (k<0)
		return 401+k;
	else
		return k;
}
int getf(int x){
	return fa[x]==x?x:fa[x]=getf(fa[x]);
}
int main(){
	for (int i=1;i<=m;i++)
		fa[i]=i;
	n=read();
	read();
	while (n--){
		int a=read(),b=read(),c=read(),d=read();
		int x=c?-c:a;
		int y=d?d:-b;
		x=_(x),y=_(y);
		fa[getf(x)]=getf(y);
		in[y]++,out[x]++;
	}
	for (int i=1;i<=m;i++){
		if (!in[i]&&!out[i])
			continue;
		cnt[getf(i)]++;
		if (in[i]!=out[i])
			f[getf(i)]=1;
	}
	for (int i=1;i<=200;i++)
		if (out[i]<in[i]||in[401-i]<out[401-i])
			return puts("NO"),0;
	for (int i=1;i<=m;i++)
		if (cnt[i]&&!f[i])
			return puts("NO"),0;
	puts("YES");
	return 0;
}