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>
using namespace std;
const int maxn = 440;
int n, c, d, l, r, deg[maxn], vis[maxn];
vector<int> g[maxn];
void add_edge(int l, int r) {
	l += maxn/2, r += maxn/2;
	deg[l]++, deg[r]--;
	g[l].push_back(r);
}
void dfs(int v) {
	vis[v] = 1;
	for(auto &i : g[v]) if(!vis[i]) dfs(i);
}
bool check() {
	dfs(0);
	for(int i = 0; i < maxn; i++) if(g[i].size() && (!vis[i] || deg[i])) return false;
	return true;
}
int main() {
	cin >> n >> r;
	map<int, int> L, R;
	while(n--) {
		cin >> l >> r >> c >> d;
		if(c > 0) l = -c;
		if(d > 0) r = -d;
		add_edge(l, -r);
		if(l < 0) R[-l]--;
		else L[l]++;
		if(r < 0) L[-r]--;
		else R[r]++;
	}
	for(auto i : L) {
		if(i.second < 0) return cout << "NO", 0;
		while(i.second--) add_edge(-220, i.first);
	}
	for(auto i : R) {
		if(i.second < 0) return cout << "NO", 0;
		while(i.second--) add_edge(-i.first, -220);
	}
	cout << (check()?"YES":"NO");
}
