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 <iostream>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <vector>
#include <queue>
#include <stack>
#include <cmath>

using namespace std;

const int MAXN = 100000 + 1000;
const int ZERO = 250;

int n, h;
int fa[MAXN], deg[MAXN], vis[MAXN], ok[MAXN];

int find(int x)
{
	return x == fa[x] ? x : fa[x] = find(fa[x]);
}

void unite(int x, int y)
{
	fa[find(x)] = find(y);
}

void no()
{
	cout << "NO" << endl;
	exit(0);
}

void yes()
{
	cout << "YES" << endl;
	exit(0);
}

int main()
{
	ios::sync_with_stdio(false);
	// freopen("1.in", "r", stdin);
	// freopen("1.out", "w", stdout);

	cin >> n >> h;
	for(int i = -h + ZERO; i <= h + ZERO; i++)
		fa[i] = i;
	for(int i = 1; i <= n; i++)
	{
		int a, b, c, d, l, r;
		cin >> a >> b >> c >> d;
		l = (c == 0 ? a : -c);
		r = (d == 0 ? -b : d);
		deg[l + ZERO]++, vis[l + ZERO]++;
		deg[r + ZERO]--, vis[r + ZERO]++;
		unite(l + ZERO, r + ZERO);
		// cerr << l << ' ' << r << endl;
	}
	for(int i = -h + ZERO; i <= -1 + ZERO; i++)
		if(deg[i] > 0)
			no();
	for(int i = 1 + ZERO; i <= h + ZERO; i++)
		if(deg[i] < 0)
			no();
	for(int i = -h + ZERO; i <= h + ZERO; i++)
		if(deg[i] != 0)
			ok[find(i)] = true;
	for(int i = -h + ZERO; i <= h + ZERO; i++)
		if(find(i) == i && vis[i] && !ok[i])
			no();
	yes();

	return 0;
}
