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Contest: Task: Related: TaskD TaskF

Score : $1200$ points

Problem Statement

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.

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.

Sample Input 1

3 4
1 1 0 0
2 2 0 1
3 3 1 0

Sample Output 1

YES

The figure below shows a possible arrangement.

Sample Input 2

4 2
1 1 0 1
1 1 0 1
1 1 0 1
1 1 0 1

Sample Output 2

NO

Sample Input 3

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

Sample Output 3

YES