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 e1 first
#define e2 second
#define pb push_back
#define mp make_pair
#define boost ios_base::sync_with_stdio(false)
#define eb emplace_back
#define OUT(x) {cout << x; exit(0); }
#define FOR(i, a, b) for(int i=(a); i<=(b); ++i)
typedef long long ll;
typedef unsigned long long ull;
typedef pair <int, int> PII;
typedef pair <ll, ll> PLL;
typedef pair <PLL, PLL> PP;
typedef pair <PII, int> PPI;
typedef unsigned int ui;
typedef vector <int> vi;
const ll mod = 1e9+7;
const int inf = 1e9+9;
const ll MOD = 1e9+696969;
const ll INF = 1e18;

const int C = 400, maxn = 1000;
vector <int> v[maxn];
int in[maxn], out[maxn], n, h, a, b, c, d;

inline void addEdge(int x, int y)
{
	v[x].pb(y);
	v[y].pb(x);
	in[y]++;
	out[x]++;
}
bool ans = 0;
bool odw[maxn];
void dfs(int x)
{
	odw[x] = 1;
	if (in[x] != out[x]) ans = 1;
	for (auto u : v[x])
		if (!odw[u]) dfs(u);
}
int main()
{
	boost;
	cin >> n >> h;
	FOR(i, 1, n)
	{
		cin >> a >> b >> c >> d;
		int l = (c == 0)?a:-c, r = (d == 0)?-b:d;
		addEdge(l + C, r + C);
	}
	
	FOR(i, 1, h)
		if (in[i + C] > out[i + C]) OUT("NO");
	
	FOR(i, -h, -1)
		if (in[i + C] < out[i + C]) OUT("NO");
	
	FOR(i, -h, h)
		if (!odw[i + C] && (int)v[i + C].size() > 0) 
		{
			ans = 0;
			dfs(i + C);
			if (!ans) OUT("NO");
		}
	cout << "YES";
}
