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;
#define inf 2123333333

int fa[1010],in[1010],out[1010],n,h;
bool bo[1010];

inline int rd()
{
	int x=0;char ch=getchar();
	for (;ch<'0'||ch>'9';ch=getchar());
	for (;ch>='0'&&ch<='9';ch=getchar()) x=x*10+ch-'0';
	return x;
}

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

int main()
{
	n=rd();h=rd();
	for (int i=1;i<=h*2;i++) fa[i]=i;
	for (int i=1;i<=n;i++)
	{
		int h1=rd(),h2=rd(),h3=rd(),h4=rd();
		int x=(!h3)?h1:h3+h,y=(!h4)?h2+h:h4;
		out[x]++;in[y]++;
		int f1=find(x),f2=find(y);
		if (f1!=f2) fa[f1]=f2;
	}
	for (int i=1;i<=h;i++) if (in[i]>out[i]) { puts("NO");return 0; }
	for (int i=h+1;i<=h*2;i++) if (in[i]<out[i]) { puts("NO");return 0; }
	for (int i=1;i<=h*2;i++) if (in[i]^out[i]) bo[find(i)]=true;
	for (int i=1;i<=h*2;i++) if (!bo[find(i)]) if (in[i]||out[i]) { puts("NO");return 0; }
	puts("YES");
	return 0;
}