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

$1\le N,K\le {10}^9$

$1\le M\le {10}^4$

$0\le a_i\le b_i\le N$

$1\le t_i\le {10}^4$

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