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 <algorithm>
#include <iostream>
#include <cstring>
#include <cstdio>
#include <cmath>
using namespace std;

inline int getint()
{
	static char c;
	while ((c = getchar()) < '0' || c > '9');

	int res = c - '0';
	while ((c = getchar()) >= '0' && c <= '9')
		res = res * 10 + c - '0';
	return res;
}

const int MaxN = 100000;
const int MaxM = 200;
const int MaxNV = MaxM * 2;

int n, m;
int in[MaxNV + 1], out[MaxNV + 1];

int ufs[MaxNV + 1];

int ufs_find(int v)
{
	return ufs[v] == v ? v : ufs[v] = ufs_find(ufs[v]);
}

int main()
{
	cin >> n >> m;

	for (int u = 1; u <= m + m; ++u)
		ufs[u] = u;

	for (int i = 0; i < n; ++i)
	{
		int a = getint(), b = getint();
		int c = getint(), d = getint();

		int u = c ? c + m : a;
		int v = d ? d : m + b;

		++out[u], ++in[v];

		ufs[ufs_find(v)] = ufs_find(u);
	}

	bool ok = true;

	for (int u = 1; u <= m; ++u)
		if (out[u] < in[u])
			ok = false;

	for (int v = 1; v <= m; ++v)
		if (out[v + m] > in[v + m])
			ok = false;

	for (int u = 1; u <= m + m; ++u)
		if (ufs[u] == u && (in[u] || out[u]))
		{
			bool all = true;
			for (int v = 1; v <= m + m; ++v)
				if (ufs_find(v) == u)
					all &= in[v] == out[v];

			if (all)
				ok = false;
		}

	puts(ok ? "YES" : "NO");

	return 0;
}