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;

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

#define F first
#define S second

const int MAXN = 1e5 + 10;

int n, h, c1[MAXN], c0[MAXN];
bool vis[MAXN];
vector<int> adj[MAXN];
bool found = 0;

void dfs(int v){
	vis[v] = 1;
	if (c0[v] ^ c1[v]) found = 1;
	if ((v > h && c1[v] > c0[v]) || (v <= h && c0[v] > c1[v])){
		cout << "NO\n";
		exit(0);
	}
	for (int u:adj[v])
		if (!vis[u])
			dfs(u);
}

int main(){
	ios::sync_with_stdio(false);
	cin.tie(0);
	cin >> n >> h;
	while (n--){
		int a, b, c, d; cin >> a >> b >> c >> d;
		int u = -1, v = -1;
		if (c == 0)
			u = a;
		else
			u = h+c;
		if (d)
			v = d;
		else
			v = h+b;
		adj[u].push_back(v);
		c1[u]++;
		adj[v].push_back(u);
		c0[v]++;
	}
	for (int i = 1; i <= h+h; i++)
		if (!vis[i] && adj[i].size()){
			found = 0;
			dfs(i);
			if (!found){
				cout << "NO\n";
				return 0;
			}
		}
	cout << "YES\n";
	return 0;
}
