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 <cstdio>
#include <vector>
using namespace std;

#define iter(i, n) for (int i = 1; i <= n; ++i)

#define PR 510

vector<int> e[PR];
bool invalid, vis[PR], start;
int sum, deg[PR], n, h;

void dfs(int x) {
	vis[x] = true;
	sum += deg[x];
	if (deg[x] != 0) {
		start = true;
		if ((deg[x] > 0) != (x <= h)) invalid = true;
	}
	for (int v : e[x]) if (!vis[v]) dfs(v);
}

int main() {
	scanf("%d%d", &n, &h);
	iter(i, 2 * h) vis[i] = true;
	iter(i, n) {
		int a, b, c, d;
		scanf("%d%d%d%d", &a, &b, &c, &d);
		int u = c == 0 ? a : c + h;
		int v = d == 0 ? b + h : d;
		e[u].push_back(v);
		e[v].push_back(u);
		//printf("%d->%d\n", u, v);
		++deg[u], --deg[v]; vis[u] = vis[v] = false;
	}

	//iter(i, 2 * h) printf("%d ", deg[i]);

	iter(i, 2 * h) if (!vis[i]) {
		start = false; dfs(i);
		if (sum != 0 || !start) invalid = true;
	}

	puts(invalid ? "NO" : "YES");
	return 0;
}
