A shuttle drives along a straight route and has a fixed seat capacity C. There are n trips; trip i boards p passengers at milepost s and drops them at milepost e (with s < e), so those passengers occupy seats over the half-open range [s, e). Because a passenger leaving at milepost e frees the seat exactly at e, a trip ending at e and another starting at e do not overlap. Determine whether the number of onboard passengers stays at or below C at every point of the route.

Input format

Line 1: two integers n and C. Next n lines: three integers p, s, e describing one trip (1 ≤ p, 0 ≤ s < e).

Output format

Print YES if the capacity is never exceeded, otherwise NO.

Constraints

• 1 ≤ n ≤ 100000
• 1 ≤ C ≤ 1000000000
• 1 ≤ p ≤ 1000000
• 0 ≤ s < e ≤ 1000000000

2 3
2 1 5
2 3 7

NO

2 4
2 1 5
2 3 7

YES