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 <cstdio>
#include <cstring>
#define MAXN 1000010

int n,h;
int g[MAXN],nume;
int p[MAXN][2],nump;
int d[MAXN],size[MAXN],sd[MAXN][2];
bool tag[MAXN];
int f[MAXN];

int getf(int x){
	if(f[x]==x) return x;
	return f[x]=getf(f[x]);
}

int main(){
#ifdef DEBUG
	freopen("E.in","r",stdin);
#endif
	for(int i=1;i<MAXN;i++) f[i]=i;
	memset(g,-1,sizeof g);
	scanf("%d%d",&n,&h);
	for(int i=1;i<=h;i++) p[i][0]=++nump;
	for(int i=1;i<=h;i++) p[i][1]=++nump;
	for(int i=1;i<=n;i++){
		int t1,t2,t3,t4,u,v;
		scanf("%d%d%d%d",&t1,&t2,&t3,&t4);
		if(!t3) u=p[t1][1];
		else u=p[t3][0];
		if(!t4) v=p[t2][0];
		else v=p[t4][1];
		if(getf(u)^getf(v)) f[f[u]]=f[v];
		d[u]--;
		d[v]++;
		tag[u]=tag[v]=1;
	}
	for(int i=1;i<=n;i++) 
		if(d[p[i][0]]<0 || d[p[i][1]]>0){
			puts("NO");
			return 0;
		}
	for(int i=1;i<=nump;i++){
		size[getf(i)]++;
		if(d[i]<0) sd[getf(i)][0]+=-d[i];
		else sd[getf(i)][1]+=d[i];
		if(tag[i]) tag[getf(i)]=1;
	}
	int numc=0;
	int s0=0,s1=0;
	for(int i=1;i<=nump;i++)
		if(getf(i)==i && tag[i]){
			if(!sd[i][0] && !sd[i][1]){
				puts("NO");
				return 0;
			}
			s0+=sd[i][0];
			s1+=sd[i][1];
			numc++;
		}
	if(s0^s1){
		puts("NO");
		return 0;
	}
	if(s0<numc-1){
		puts("NO");
		return 0;
	}
	puts("YES");
	return 0;
}
