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<algorithm>
const int N=1005,M=2e5+5;
const int Z=205;
using namespace std;
int n,h;
int rudu[N],chudu[N];
bool vis[N];
struct node{
    int u,v,nxt;
}edge[M];
int head[N],mcnt;
void add_edge(int u,int v){
	mcnt++;
	edge[mcnt].u=u;
    edge[mcnt].v=v;
    edge[mcnt].nxt=head[u];
    head[u]=mcnt;
    rudu[v]++;
    chudu[u]++;
}
void dfs(int u){
	vis[u]=true;
	for(int i=head[u];i;i=edge[i].nxt){
        int v=edge[i].v;
		if(!vis[v])
            dfs(v);
	}
}
int main()
{
	scanf("%d%d",&n,&h);
	for(int i=1;i<=n;i++){
		int a,b,c,d,l,r;
		scanf("%d%d%d%d",&a,&b,&c,&d);
		l=c?(-c):a;
		r=d?d:(-b);
		add_edge(l+Z,r+Z);
	}
	for(int i=Z-h;i<Z;i++)
		if(rudu[i]<chudu[i]){
            puts("NO");
            return 0;
        }
	for(int i=Z+1;i<=Z+h;i++)
		if(rudu[i]>chudu[i]){
            puts("NO");
            return 0;
        }
	for(int i=Z-h;i<=Z+h;i++)
		if(chudu[i]>rudu[i]&&!vis[i])
            dfs(i);
	for(int i=Z-h;i<=Z+h;i++)
		if((rudu[i]||chudu[i])&&!vis[i]){
            puts("NO");
            return 0;
        }
	puts("YES");
}
