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<vector>
using namespace std;
inline int read()
{
	int x;char c;
	while((c=getchar())<'0'||c>'9');
	for(x=c-'0';(c=getchar())>='0'&&c<='9';)x=x*10+c-'0';
	return x;
}
#define MN 100000
#define MX 200
int d1[MX*2+5],d2[MX*2+5],f[MX*2+5];
vector<int> v[MX*2+5];
int gf(int k){return f[k]?f[k]=gf(f[k]):k;}
int main()
{
	int n,i,j,a,b,c,d;
	n=read();read();
	for(i=1;i<=n;++i)
		a=read(),b=read(),c=read(),d=read(),a=(c?-c:a)+MX,b=(d?d:-b)+MX,
		++d1[a],++d2[b],gf(a)!=gf(b)?f[gf(a)]=gf(b):0;
	for(i=1;i<=MX<<1;++i)if(d1[i]||d2[i])v[gf(i)].push_back(i);
	for(i=1;i<=MX<<1;++i)if(v[i].size())
	{
		for(j=a=b=0;j<v[i].size();++j)
			if(v[i][j]>MX)
			{
				if(d1[v[i][j]]<d2[v[i][j]])return 0*puts("NO");
				a+=d1[v[i][j]]-d2[v[i][j]];
				b|=d1[v[i][j]]-d2[v[i][j]];
			}
			else
			{
				if(d2[v[i][j]]<d1[v[i][j]])return 0*puts("NO");
				a+=d1[v[i][j]]-d2[v[i][j]];
			}
		if(!b||a)return 0*puts("NO");
	}
	puts("YES");
}