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>
#include <cstring>
#include <algorithm>
using namespace std;
typedef long long ll;
const int maxn=512;
const int zero=250;
int fa[maxn],siz[maxn],oud[maxn],ind[maxn];
bool h[maxn];
int find(int k)
{
	if(fa[k]!=k)fa[k]=find(fa[k]);
	return fa[k];
}
inline int read(){
	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 void merge(int x,int y){
    x=find(x);y=find(y);
    if(x==y){++siz[x];return;}
    fa[x]=y;siz[y]+=siz[x] + 1;
}
int main(){
    int n,H;n=read();H=read();
    for(int i=1;i<=H;i++)  fa[i+zero]= i+zero,siz[i+zero]= 1;
    for(int i=-H;i<=-1;i++)fa[i+zero]= i+zero,siz[i+zero]= 1;
    int a,b,c,d;
    for(int i=1;i<=n;i++){
        int x,y;
        a=read();b=read();c=read();d=read();
        if(c==0)x=a;else x=-c;
        if(d==0)y=-b;else y=d;
        ++oud[x+ zero];++ ind[y + zero];
        merge(x+zero,y+zero);
    }
    for(int i=1;i<=H;i++)  if(oud[i+zero]<ind[i+zero])return puts("NO"),0;
    for(int i=-H;i<=-1;i++)if(ind[i+zero]<oud[i+zero])return puts("NO"),0;
    for(int i=1;i<=H;i++)  h[find(i+zero)]|=(ind[i+zero]!=oud[i+zero]);
    for(int i=-H;i<=-1;i++)h[find(i+zero)]|=(ind[i+zero]!=oud[i+zero]);
    for(int i=1;i<=H;i++)  if(siz[find(i+zero)]>1&&(find(i+zero)==i+zero)&&(h[i+zero]==false))return puts("NO"),0;
    for(int i=-H;i<=-1;i++)if(siz[find(i+zero)]>1&&(find(i+zero)==i+zero)&&(h[i+zero]==false))return puts("NO"),0;
    puts("YES");
    return 0;
}