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<iostream>
#include<vector>
#include<algorithm>
#include<cstring>
#include<cstdio>
#include<cmath>
#include<cstdlib>
#include<ctime>
#include<queue>
#include<set>
#include<map>
#include<stack>
#include<bitset>
using namespace std;
typedef long long LL;
int gi() {
	int w=0;bool q=1;char c=getchar();
	while ((c<'0'||c>'9') && c!='-') c=getchar();
	if (c=='-') q=0,c=getchar();
	while (c>='0'&&c <= '9') w=w*10+c-'0',c=getchar();
	return q? w:-w;
}
const int N=1e5;
int fa[N];inline int find(int x) { return fa[x]==x?x:fa[x]=find(fa[x]); }
int in[N],out[N];
bool vis[N],f[N],g[N];
int main()
{
	int n=gi(),a,b,c,d,l,r,i;gi();
	for (i=0;i<=400;i++) fa[i]=i;
	for (i=1;i<=n;i++) {
		a=gi(),b=gi(),c=gi(),d=gi();
		l=c?-c:a;
		r=d?d:-b;
		l+=200,r+=200;
		out[l]++,in[r]++;
		vis[l]=vis[r]=true;
		fa[find(l)]=find(r);
	}
	for (i=0;i<200;i++)
		if (out[i]>in[i]) return puts("NO"),0;
		else if (out[i]!=in[i]) f[find(i)]=true;
	for (i=201;i<=400;i++)
		if (in[i]>out[i]) return puts("NO"),0;
		else if (out[i]!=in[i]) g[find(i)]=true;
	for (i=0;i<=400;i++)
		if (vis[i]&&fa[i]==i&&(!g[i]||!f[i])) return puts("NO"),0;
	puts("YES");
	return 0;
}
