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>

using namespace std;
const int N = 1e6;

int n, h;
int a[N], b[N], c[N], d[N], vis[N], in[N], out[N], fa[N];

int read(void) {
    int s = 0, w = 0;
    char c = getchar();
    while (c < '0' || c > '9') w |= c == '-', c = getchar();
    while (c >= '0' && c <= '9') s = s * 10 + c - 48, c = getchar();
    return w ? -s : s;
}

int get(int x) {
	if (fa[x] == x) return x;
	return fa[x] = get(fa[x]); 
}

bool check(void)
{
	for (int i=-h;i<0;++i) 
		if (in[i+h] > out[i+h]) return 0;
	for (int i=1;i<=h;++i)
	    if (in[i+h] < out[i+h]) return 0;
	for (int i=-h;i<=h;++i)
	    if (in[i+h] != out[i+h]) vis[get(i+h)] = 1;
	    else if (in[i+h] +out[i+h] == 0) vis[get(i+h)] = 1;
	for (int i=-h;i<=h;++i)
		if (vis[get(i+h)] == 0) return 0;
	return 1;
	
}

int main(void)
{
	n = read(), h = read();
	for (int i=0;i<=1000;++i) fa[i] = i;
	for (int i=1;i<=n;++i)
	{
		a[i] = read(); b[i] = read();
		c[i] = read(); d[i] = read();
		int x = c[i] == 0 ? h-a[i] : h+c[i];
		int y = d[i] == 0 ? h+b[i] : h-d[i];
		out[x] ++, in[y] ++;
		fa[get(x)] = get(y);
	}
	if (check()) cout << "YES";
	else cout << "NO";
	return 0;
}