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 N 409
#define M 200009
using namespace std;

int n,m,sz1,sz2,tot,fst[N],pnt[M],nxt[M],f[M],g[M]; bool vis[N];
void add(int x,int y){
	pnt[++tot]=y; nxt[tot]=fst[x]; fst[x]=tot;
}
void ins(int x,int y){
	add(x,y); add(y,x); f[y]++; g[x]++;
}
void dfs(int x){
	vis[x]=1; if (!f[x] && !g[x]) return;
	int i,y; 
	sz1+=(x<=n && f[x]<g[x]); sz2+=(x>n && f[x]>g[x]);
	if (x<=n && f[x]>g[x] || x>n && f[x]<g[x]){
		puts("NO"); exit(0);
	}
	for (i=fst[x]; i; i=nxt[i]){
		y=pnt[i];
		if (!vis[y]) dfs(y);
	}
}
int main(){
	scanf("%d%d",&m,&n);
	int i,x,y,u,v;
	while (m--){
		scanf("%d%d%d%d",&x,&y,&u,&v);
		ins(u?u+n:x,v?v:y+n);
	}
	for (i=1; i<=(n<<1); i++) if (!vis[i] && f[i]+g[i]){
		sz1=sz2=0; dfs(i);
		if (!sz1 || !sz2){ puts("NO"); return 0; }
	}
	puts("YES");
	return 0;
}
