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 <vector>
#define llint long long

using namespace std;

int n, h;
vector<llint> G[405], revG[405];
const llint Pos = 202;
bool used[405];
int S, T;

bool dfs(llint v, llint &lsum, llint &rsum)
{
	used[v] = true;
	int deg = (int)G[v].size() - (int)revG[v].size();
	if(v <= 200){
		if(deg < 0) return false;
		lsum += deg;
	}
	else{
		if(deg > 0) return false;
		rsum -= deg;
	}
	for(int i = 0; i < G[v].size(); i++){
		if(used[G[v][i]]) continue;
		if(!dfs(G[v][i], lsum, rsum)) return false;
	}
	for(int i = 0; i < revG[v].size(); i++){
		if(used[revG[v][i]]) continue;
		if(!dfs(revG[v][i], lsum, rsum)) return false;
	}
	return true;
}

int main(void)
{
	cin >> n >> h;
	llint a, b, c, d, u, v;
	for(int i = 1; i <= n; i++){
		cin >> a >> b >> c >> d;
		if(c == 0) u = a;
		else u = Pos+c;
		if(d == 0) v = Pos+b;
		else v = d;
		
		G[u].push_back(v);
		revG[v].push_back(u);
	}
	for(int i = 0; i <= 400; i++){
		if(G[i].size() == 0 && revG[i].size() == 0) used[i] = true;
	}
	
	for(int i = 0; i <= 400; i++){
		if(used[i]) continue;
		llint lsum = 0, rsum = 0;
		if(!(dfs(i, lsum, rsum) && lsum == rsum && lsum > 0)){
			cout << "NO" << endl;
			return 0;
		}
	}
	cout << "YES" << endl;
	
	return 0;
}