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 <bits/stdc++.h>
#define rep(i,n) for(int i=0;i<(int)(n);i++)
#define rep1(i,n) for(int i=1;i<=(int)(n);i++)
#define all(c) c.begin(),c.end()
#define pb push_back
#define fs first
#define sc second
#define show(x) cout << #x << " = " << x << endl
#define chmin(x,y) x=min(x,y)
#define chmax(x,y) x=max(x,y)
using namespace std;
template<class S,class T> ostream& operator<<(ostream& o,const pair<S,T> &p){return o<<"("<<p.fs<<","<<p.sc<<")";}
template<class T> ostream& operator<<(ostream& o,const vector<T> &vc){o<<"sz = "<<vc.size()<<endl<<"[";for(const T& v:vc) o<<v<<",";o<<"]";return o;}
bool solve(){
	int N,H;
	cin>>N>>H;
	vector<int> deg(2*H+3);
	vector<bool> is(2*H+3,false);
	int S = 2*H+2;
	int V = 2*H+3;
	is[S] = true;

	bool e[403][403]={};
	rep(i,V) e[i][i] = 1;


	rep(i,N){
		int a,b,c,d;
		cin>>a>>b>>c>>d;
		int s = (c==0?a:H+1+c);
		int t = (d==0?H+1+b:d);
		deg[s]++;
		deg[t]--;
		e[s][t] = 1;
		is[s] = 1;
		is[t] = 1;
	}
	rep(i,H+1){
		if(deg[i]<0) return 0;
		if(deg[i]>0) e[S][i] = 1;
		if(deg[i+H+1]>0) return 0;
		if(deg[i+H+1]<0) e[i+H+1][S] = 1;
	}
	rep(i,V) rep(j,V) rep(k,V) if(e[j][i]&&e[i][k]) e[j][k] = 1;
	rep(i,V) if(is[i]){
		if(!(e[S][i]&&e[i][S])) return 0;
	}
	return 1;
}
int main(){
	if(solve()) puts("YES");
	else puts("NO");
}
