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 i64;

const int MAXN = (200 + 10) * 2;

class no_solution : public std::exception
{
public:
	const char * what(void) const noexcept
	{
		return "no solution reachable";
	}
};

namespace disjointSet
{
int fa[MAXN];

void init()
{
	memset(fa, 0x00, sizeof fa);
}

int find(int x)
{
	if(fa[x])
		return fa[x] = find(fa[x]);
	return x;
}

void merge(int x, int y)
{
	x = find(x), y = find(y);
	if(x != y)
		fa[x] = y;
}

}

bool loop[MAXN];
int inDeg[MAXN], outDeg[MAXN];
int N, H;

void solve()
{
	for(int i = 0; i <= 2 * H; i++)
	{
		if(i > H)
			if(inDeg[i] > outDeg[i])
				throw no_solution();
		if(i < H)
			if(outDeg[i] > inDeg[i])
				throw no_solution();

		bool found = false, isLoop = loop[i];

		for(int j = 0; j <= 2 * H; j++)
			if(found)
				break;
			else
				if(disjointSet::find(i) == disjointSet::find(j))
				{
					if(i != j)
						isLoop = true;
					if(inDeg[j] != outDeg[j])
						found = true;
				}

		if(!found && isLoop)
			throw no_solution();
	}
}

int main()
{
	ios::sync_with_stdio(false), cin.tie(nullptr);

	cin >> N >> H ;
	for(int i = 1; i <= N; i++)
	{
		int a, b, c, d, L, R;
		cin >> a >> b >> c >> d;
		L = c ? H - c : H + a;
		R = d ? H + d : H - b;
		disjointSet::merge(L, R);
		inDeg[R]++, outDeg[L]++;

		if(L == R)
			loop[L] = true;
	}


	try
	{
		solve();
		cout << "YES" << endl;
	}
	catch(std::exception & x)
	{
		cout << "NO" << endl ;
	}

	return 0;
}

