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