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>
#define mo 10007
#define pi 3.1415926535898
#define eps 1e-9 
using namespace std;
long long read(){
    long long xx=0,flagg=1;
    char ch=getchar();
    while((ch<'0'||ch>'9')&&ch!='-')
        ch=getchar();
    if(ch=='-'){
        flagg=-1;
        ch=getchar();
    }
    while(ch>='0'&&ch<='9'){
        xx=xx*10+ch-'0';
        ch=getchar();
    }
    return xx*flagg;
}
void pus(long long xx,long long flagg){
    if(xx<0){
        putchar('-');
        xx=-xx;
    }
    if(xx>=10)
        pus(xx/10,0);
    putchar(xx%10+'0');
    if(flagg==1)
        putchar(' ');
    if(flagg==2)
        putchar('\n');
    return;
}
int n,h,i,zz[405],ru[405],chu[405],book[405],a,b,c,d;
int zzz(int z){
	if(zz[z]==z) return z;
	return zz[z]=zzz(zz[z]);
}
int main(){
	n=read();h=read();
	for(i=1;i<=h*2;i++)
		zz[i]=i;
	for(i=1;i<=n;i++){
		a=read();b=read();c=read();d=read();
		if(c==0)
			c=a;
		else
			c+=h;
		if(d==0)
			d=b+h;
		chu[c]++;
		ru[d]++;
		c=zzz(c);
		d=zzz(d);
		if(zz[c]!=d)
			zz[c]=d;
	}
	for(i=1;i<=h;i++)
		if(ru[i]>chu[i]||ru[i+h]<chu[i+h]){
			printf("NO\n");
			return 0;
		}
	for(i=1;i<=h*2;i++)
		if(ru[i]!=chu[i]||ru[i]==0&&chu[i]==0)
			book[zzz(i)]=1;
	for(i=1;i<=h*2;i++)
		if(zz[i]==i&&book[i]==0){
			printf("NO\n");
			return 0;
		}
	printf("YES\n");
   	return 0;
}