#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
using namespace std;
#define N 405
int n, h, ins[N], out[N], bel[N];
bool flg[N];
int Getbel(int x){return bel[x] == x ? x : bel[x] = Getbel(bel[x]);}
int main()
{
	scanf("%d%d", &n, &h);
	for (int i = 1; i <= (h << 1); i++)
		bel[i] = i;
	for (int i = 1; i <= n; i++)
	{
		int a, b, c, d;
		scanf("%d%d%d%d", &a, &b, &c, &d);
		int x = c ? c + h : a, y = d ? d : b + h;
		out[x]++, ins[y]++;
		x = Getbel(x), y = Getbel(y);
		if (x != y)
			bel[x] = y;
	}
	for (int i = 1; i <= h; i++)
		if (ins[i] > out[i])
		{
			puts("NO");
			return 0;
		}
	for (int i = h + 1; i <= (h << 1); i++)
		if (ins[i] < out[i])
		{
			puts("NO");
			return 0;
		}
	for (int i = 1; i <= (h << 1); i++)
		if (ins[i] != out[i] || (!ins[i] && !out[i]))
			flg[Getbel(i)] = 1;
	for (int i = 1; i <= (h << 1); i++)
	{
		if (bel[i] == i && !flg[i])
		{
			puts("NO");
			return 0;
		}
	}
	puts("YES");
}

### Prompt

Please formulate a CPP solution to the following problem:

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.



<image>

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

### Response

```cpp
#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
using namespace std;
#define N 405
int n, h, ins[N], out[N], bel[N];
bool flg[N];
int Getbel(int x){return bel[x] == x ? x : bel[x] = Getbel(bel[x]);}
int main()
{
	scanf("%d%d", &n, &h);
	for (int i = 1; i <= (h << 1); i++)
		bel[i] = i;
	for (int i = 1; i <= n; i++)
	{
		int a, b, c, d;
		scanf("%d%d%d%d", &a, &b, &c, &d);
		int x = c ? c + h : a, y = d ? d : b + h;
		out[x]++, ins[y]++;
		x = Getbel(x), y = Getbel(y);
		if (x != y)
			bel[x] = y;
	}
	for (int i = 1; i <= h; i++)
		if (ins[i] > out[i])
		{
			puts("NO");
			return 0;
		}
	for (int i = h + 1; i <= (h << 1); i++)
		if (ins[i] < out[i])
		{
			puts("NO");
			return 0;
		}
	for (int i = 1; i <= (h << 1); i++)
		if (ins[i] != out[i] || (!ins[i] && !out[i]))
			flg[Getbel(i)] = 1;
	for (int i = 1; i <= (h << 1); i++)
	{
		if (bel[i] == i && !flg[i])
		{
			puts("NO");
			return 0;
		}
	}
	puts("YES");
}

```