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 <bits/stdc++.h>

using namespace std;

using ll = long long;
using vi = vector<int>;
using db = double;
#define pb push_back

#define ass(x) ({if(!(x)) return false;})

const int mxn = 206;

int n, h;
unordered_map<int,int> deg;
unordered_map<int,bool> v;

struct DSU {
	unordered_map<int,int> p;
	void clear() {
		for (int i = -200; i <= 200; ++i)
			p[i] = i;
	}
	int root(int x) {
		return p[x] == x ? x : p[x] = root(p[x]);
	}
	void merge(int x, int y) {
		p[root(x)] = root(y);
	}
	int operator[](int x) { return root(x); }
} U;

unordered_map<int,int> f;

bool connected() {
	for (int i = -200; i <= 200; ++i)
		f[U[i]] |= deg[i] < 0 ? 1 : deg[i] > 0 ? 2 : 0;
	for (int i = -200; i <= 200; ++i) if (v[i])
		ass(f[U[i]] == 3);
	return true;
}

bool check() {
	for (int i = -200; i <= 200; ++i)
		ass(deg[i] * i >= 0);
	return true;
}

int main() {
	cin >> n >> h;
	
	U.clear();
	
	for (int i = 1; i <= n; ++i) {
		int a, b, c, d;
		scanf("%d%d%d%d", &a, &b, &c, &d);
		int x, y;
		x = c ? -c : a;
		y = d ? -d : b;
		y = -y;
		++deg[x];
		--deg[y];
		v[x] = v[y] = true;
		U.merge(x, y);
		//cout << x << ' ' << y << endl;
	}
	
	puts(check() && connected() ? "YES" : "NO");
	
	return 0;
}
