Restaurant Reservation Capacity Check

You are given a restaurant with a seating capacity of \( m \) and \( n \) reservations. Each reservation is described by three integers \( s_i \), \( e_i \), and \( g_i \), representing the start time, end time (in minutes past midnight), and the number of guests for that reservation respectively. The restaurant operates with a discrete minute granularity from 0 to 1440. Your task is to determine whether the restaurant can accommodate all the reservations without ever exceeding its seating capacity.

Formally, for each minute \( t \) in the interval \([0, 1440]\), compute the total number of guests present by summing \( g_i \) for all reservations where \( s_i \leq t < e_i \). The condition to check is: \[ \text{current guests}(t) \leq m \quad \text{for all } t \in [0,1440] \]

If the condition holds, print Yes; otherwise, print No.

inputFormat

The input is given via standard input in the following format:

n m
s1 e1 g1
s2 e2 g2
... 
sn en gn

Where:

• n is the number of reservations,
• m is the seating capacity,
• Each of the next n lines contains three integers: \( s_i \) (start time), \( e_i \) (end time) and \( g_i \) (number of guests).

outputFormat

Output a single line to standard output containing Yes if the restaurant can accommodate all reservations without exceeding the capacity at any moment, or No otherwise.

3 10
0 60 4
30 90 5
70 120 3

Yes