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 <algorithm>
#include <cstdio>
#include <cstring>
#include <queue>
#include <vector>
#include <bitset>
#include <string>
#include <cmath>
#include <set>
#include <map>
#define Rep(i, x, y) for (int i = x; i <= y; i ++)
#define Dwn(i, x, y) for (int i = x; i >= y; i --)
#define RepE(i, x) for (int i = pos[x]; i; i = g[i].nex)
#define ev g[i].y
#define eps 1e-10
using namespace std;
typedef long long ll;
typedef double db;
const int N = 100005, mod = 1000000007;
int n, m, ind[N], outd[N], pos[N], sz;
bool vis[N], fl;
struct edge { int y, nex; } g[N * 2];
void init(int x, int y) { g[++ sz] = (edge) { y, pos[x] }, pos[x] = sz; }
int node(int x, int y) {
	return !y ? x : -y;
}
void dfs(int x) {
	vis[x] = 1;
	RepE(i, x) if (!vis[ev]) dfs(ev);
}
int main()
{
	scanf ("%d%d", &m, &n);
	Rep(i, 1, m) {
		int a, b, c, d;
		scanf ("%d%d%d%d", &a, &b, &c, &d);
		int x = node(a, c), y = -node(b, d);
		if (x < 0) x = n + (-x);
		if (y < 0) y = n + (-y);
		ind[y] ++;
		outd[x] ++;
		// cout << x<<" "<<y<<endl;
		init(x, y);
	}
	Rep(i, 1, n) {
		if (ind[i] > outd[i]) fl = 1;
		if (ind[i + n] < outd[i + n]) fl = 1;
	}
//	cout << fl<<endl;
	Rep(i, 1, n * 2) {
		if (ind[i] == outd[i]) continue ;
		if (!vis[i]) dfs(i);
	}
	Rep(i, 1, n * 2) if (ind[i] && !vis[i]) fl = 1;
	puts(fl ? "NO" : "YES");

	return 0;
}