The sky darkens... it is raining geese. Oli is on a strip of land that is ~N~ units long. He initially starts at unit ~0~ on the left, and every second he can teleport an integer from ~0~ to ~K~ units, either left or right. He cannot travel beyond unit ~N~ or beyond unit ~0~ on the strip. ~M~ squadrons of geese will rain from the sky. The ~i~th squadron hits the ground in ~t_i + 0.5~ seconds from now, temporarily vaporizing the area stretching from units ~a_i~ to ~b_i~ inclusive. Can he avoid all the geese without getting vaporized? The strip when ~N=12~ is shown below.

Constraints

~1 \leq N, K \leq 10^9~

~1 \leq M \leq 10^4~

~0 \leq a_i \leq b_i \leq N~

~1 \leq t_i \leq 10^4~

Input Specification

The first line of input contains ~3~ space-separated integers, ~N~, ~M~, and ~K~.

The next ~M~ lines each contain ~3~ space-separated integers, ~a_i~, ~b_i~, and ~t_i~. These will be sorted in increasing order of ~t_i~, all times are distinct.

Output Specification

Output a single line containing YES if he can survive and NO if he cannot.

Sample Input 1

1000 2 1
300 600 1000
0 400 1001

Sample Output 1

YES

Sample Input 2

10 6 1
0 4 11
3 7 12
8 10 13
1 2 15
4 9 16
1 7 17

Sample Output 2

YES

Sample Input 3

5 3 3
0 0 1
2 5 2
0 4 3

Sample Output 3

NO