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 xx first
#define yy second
#define mp make_pair
#define pb push_back
#define mset(x, y) memset(x, y, sizeof x)
#define mcpy(x, y) memcpy(x, y, sizeof x)
using namespace std;

typedef long long LL;
typedef pair < int, int > pii;

inline int Read()
{
	int x = 0, f = 1, c = getchar();
	for (; !isdigit(c); c = getchar())
		if (c == '-')
			f = -1;
	for (;  isdigit(c); c = getchar())
		x = x * 10 + c - '0';
	return x * f;
}

const int MAXN = 1005;

int n, m, deg[MAXN], ans = 1, f[MAXN], v[MAXN], e[MAXN];

inline int Find(int x) { while (x ^ f[x]) x = f[x] = f[f[x]]; return x; }

int main()
{
#ifdef wxh010910
	freopen("data.in", "r", stdin);
#endif
	n = Read(), m = Read();
	for (int i = 1; i <= 1000; i ++)
		f[i] = i;
	while (n --)
	{
		int a = Read(), b = Read(), c = Read(), d = Read(), x = (!c ? a : -c) + 500, y = (!d ? -b : d) + 500;
		f[Find(x)] = Find(y);
		deg[x] ++; deg[y] --; v[x] = 1;
	}
	for (int i = 0; i < 500; i ++)
		if (deg[i] > 0)
			ans = 0;
	for (int i = 501; i <= 1000; i ++)
		if (deg[i] < 0)
			ans = 0;
	for (int i = 1; i <= 1000; i ++)
		v[Find(i)] |= v[i], e[Find(i)] |= deg[i] != 0;
	for (int i = 1; i <= 1000; i ++)
		if (Find(i) == i && v[i] && !e[i])
			ans = 0;
	return puts(ans ? "YES" : "NO"), 0;
}
