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;
int par[500];
int find(int a){
	if(par[a] != a){
		par[a] = find(par[a]);
	}
	return par[a];
}

int main(){
	int n, h;
	cin >> n >> h;
	vector<int> edges[500];
	int deg[500];
	for(int i = 0; i < 500; i++){
		deg[i] = 0;
		par[i] = i;
	}
	for(int i = 0; i < n; i++){
		int a, b, c, d;
		cin >> a >> b >> c >> d;
		int v1 = c;
		int v2 = -d;
		if(c == 0) v1 = -a;
		if(d == 0) v2 = b;
		v1 += 250;
		v2 += 250;
		edges[v1].push_back(v2);
		deg[v1]++;
		deg[v2]--;
		par[find(v1)] = find(v2);
	}
	int ok = 1;
	map<int,int> c;
	for(int i = 0; i < 500; i++){
		if(deg[i] < 0 && i < 250) ok = 0;
		if(deg[i] > 0 && i > 250) ok = 0;
		if(deg[i] > 0){
			c[find(i)] = 1;
		}
	}
	for(int i = 0; i < 500; i++){
		if(edges[i].size() > 0 && c[find(i)] != 1) ok = 0;
	}
	cout << (ok ? "YES" : "NO") << endl;
}
