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.