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 512
#define ll long long
#define misaka 250
#define rep(i, h) for (int i = misaka - h; i <= h + misaka; i++) if (i)
using namespace std;
inline int read(){
	int x=0,f=1;char ch=getchar();
	while(ch>'9'||ch<'0')ch=='-'&&(f=0)||(ch=getchar());
	while(ch<='9'&&ch>='0')x=(x<<3)+(x<<1)+ch-'0',ch=getchar();
	return f?x:-x;
}
int fa[N], sz[N], out[N], ini[N], vis[N];
int find(int x){return x==fa[x]?x:fa[x]=find(fa[x]);}
void merge(int x, int y) {
	int xx = find(x), yy = find(y);
	if (xx == yy) ++ sz[xx];
	else fa[xx] = yy, sz[yy] += sz[xx] + 1;
}
int main(int argc, char const *argv[]) {
	int n = read(), h = read();
	rep(i, h) fa[i] = i, sz[i] = 1;
	for (int i = 1; i <= n; i++) {
		int a = read(), b = read(), c = read(), d = read();
		int x = (c ? -c : a) + misaka;
		int y = (d ? d : -b) + misaka;
		out[x] ++; ini[y] ++;
		merge(x, y);
	}
	for (int i = 1 + misaka; i <= h + misaka; i++)
		if (out[i] < ini[i]) return puts("NO") & 0;
	for (int i = misaka - h; i <= misaka - 1; i++)
		if (ini[i] < out[i]) return puts("NO") & 0;
	rep(i, h) vis[find(i)] |= (out[i] != ini[i]);
	rep(i, h)
		if (sz[find(i)] > 1 && find(i) == i && !vis[i])
			return puts("NO") & 0;
	puts("YES");
	return 0;
}
