Jigsaw

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.

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

inputFormat

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

outputFormat

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

样例

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

YES