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 <stdio.h>
#include <iostream>
#include <algorithm>
#include <memory.h>
#include <math.h>

using namespace std;
typedef long long LL;
const int maxn = 505;

int cnt[maxn],p[maxn],n,m,deg[maxn],usd[maxn];
int findp(int u) {return p[u]?p[u]=findp(p[u]):u;}
void no() {puts("NO");exit(0);}
int main()
{
	#ifdef Amberframe
		freopen("agc017e.in","r",stdin);
		freopen("agc017e.out","w",stdout);
	#endif
	scanf("%d %d",&n,&m);m=m<<1|1;
	for (int x,y,a,b,c,d,i=1;i<=n;i++) {
		scanf("%d %d %d %d",&a,&b,&c,&d);
		c!=0?x=c<<1|1:x=a<<1;
		d!=0?y=d<<1:y=b<<1|1;
		deg[x]++;deg[y]--;usd[x]=usd[y]=1;
		x=findp(x);y=findp(y);x!=y?p[x]=y:0;
	}
	for (int i=1;i<=m;i++)
	if (deg[i]) {
		if (deg[i]>0&&(i&1)) no();
		if (deg[i]<0&&!(i&1)) no();
	}
	for (int i=1;i<=m;i++)
		if (deg[i]>0) cnt[findp(i)]++;
	for (int i=1;i<=m;i++)
		if (usd[i]&&!p[i]&&!cnt[i]) no();
	puts("YES");
	return 0;
}