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.



<image>

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>
#include<cstring>
#include<cstdlib>
#include<algorithm>
#include<cmath>
#include<queue>
#include<vector>
#include<ctime>
#include<map>
#include<bitset>
#include<set>
#define LL long long
#define mp(x,y) make_pair(x,y)
#define pll pair<long long,long long>
#define pii pair<int,int>
using namespace std;
inline int read()
{
	int f=1,x=0;char ch=getchar();
	while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
	while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}
	return x*f;
}
int stack[20];
template<typename T>inline void write(T x)
{
	if(x<0){putchar('-');x=-x;}
    if(!x){putchar('0');return;}
    int top=0;
    while(x)stack[++top]=x%10,x/=10;
    while(top)putchar(stack[top--]+'0');
}
template<typename T>inline void pr1(T x){write(x);putchar(' ');}
template<typename T>inline void pr2(T x){write(x);putchar('\n');}
const int MAXN=405;
int n,H;
int rt[MAXN],in[MAXN],ot[MAXN],ok[MAXN],vis[MAXN];
int findrt(int x){return rt[x]==x?rt[x]:rt[x]=findrt(rt[x]);}
int main()
{
	n=read();H=read();
	for(int i=1;i<=2*H;i++)rt[i]=i;
	for(int i=1;i<=n;i++)
	{
		int a=read(),b=read(),c=read(),d=read();
		int l,r;
		if(!c)l=a;else l=-c;
		if(!d)r=-b;else r=d;
		l+=H;r+=H;
		int p=findrt(l),q=findrt(r);
		if(p!=q)rt[p]=q;
		++ot[l];++in[r];vis[l]=vis[r]=1;
	}
	for(int i=-H;i<0;i++)if(in[i+H]<ot[i+H])return puts("NO"),0;
	for(int i=1;i<=H;i++)if(in[i+H]>ot[i+H])return puts("NO"),0;
	for(int i=-H;i<0;i++)ok[findrt(i+H)]|=in[i+H]!=ot[i+H];
	for(int i=1;i<=H;i++)ok[findrt(i+H)]|=in[i+H]!=ot[i+H];
	for(int i=1;i<=2*H;i++)if(vis[i]&&!ok[findrt(i)])return puts("NO"),0;
	puts("YES");
	return 0;
}
