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>
using namespace std;
const int N=100100,M=440;
int i,j,k,n,m,h,a,b,c,d,ch,ff;
int degree[M],f[M],fg[M],z[M];
struct cc { int x,y;} A[N];
void R(int &x) {
	ff=x=0;ch=getchar();
	while (ch<'0' || '9'<ch) { if (ch=='-') ff=1;ch=getchar();}
	while ('0'<=ch && ch<='9') x=x*10+ch-'0',ch=getchar();
	if (ff) x=-x;
}
int getf(int x) {
	if (f[x]==x) return x;
	return f[x]=getf(f[x]);
}
int main() {
	R(n);R(h);
	m=h+h;
	for (i=1;i<=n;i++) {
		R(a);R(b);R(c);R(d);
		int x,y;
		if (c) x=h+c;
		else x=a;
		if (d) y=d;
		else y=h+b;
		A[i].x=x;A[i].y=y;
		degree[x]++;
		degree[y]--;
		z[x]=z[y]=1;
	}
	for (i=1;i<=h;i++) if (degree[i]<0 || degree[h+i]>0) return puts("NO"),0;
	for (i=1;i<=m;i++) {
		f[i]=i;
		if (degree[i]) fg[i]=1;
	}
	for (i=1;i<=n;i++) {
		int x=A[i].x,y=A[i].y;
		if (getf(x)!=getf(y)) {
			fg[f[y]]|=fg[f[x]];
			f[f[x]]=f[y];
		}
	}
	for (i=1;i<=m;i++) if (z[i] && !fg[getf(i)]) return puts("NO"),0;
	puts("YES");
}