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;
#define rep(i,a,b) for(int i = a; i < (b); ++i)
#define rrep(i,a,b) for(int i = b; i --> (a);)
#define all(v) v.begin(),v.end()
#define trav(x,v) for(auto &x : v)
#define sz(v) (int)(v).size()
typedef long long ll;
typedef vector<int> vi;
typedef pair<int,int> pii;

struct UF {
	vi t;
	UF(int n){
		t.resize(n,-1);
	}
	int find(int a){
		return t[a]<0 ? a : t[a] = find(t[a]);
	}
	void uni(int a, int b){
		a = find(a), b = find(b);
		if(a == b) return;
		if(t[a] < t[b]) swap(a,b);
		t[b] += t[a];
		t[a] = b;
	}
};

int main(){
	ios_base::sync_with_stdio(0);
	cin.tie(0);
	
	int n, h;
	cin >> n >> h;
	++h;
	vi as(n), bs(n), cs(n), ds(n);
	rep(i,0,n) cin >> as[i] >> bs[i] >> cs[i] >> ds[i];
	vi cnt(2*h);

	UF uf(2*h);
	vector<bool> seen(2*h);
	rep(i,0,n){
		int x = -1,y = -1;
		if(cs[i]==0) ++cnt[as[i]], x = as[i];
		else --cnt[cs[i]+h], x = cs[i]+h;
		if(ds[i]==0) ++cnt[bs[i]+h], y = bs[i]+h;
		else --cnt[ds[i]], y = ds[i];
		uf.uni(x,y);
		seen[x] = seen[y] = 1;
	}
	rep(i,0,2*h) if(seen[i] && i == uf.find(i)){
		rep(j,0,2*h)
			if(i == uf.find(j) && cnt[j] > 0)
				goto fine;
		puts("NO");
		return 0;
		fine: ;
	}
	trav(x, cnt) if(x < 0){
		puts("NO");
		return 0;
	}
	puts("YES");
}