D - Water Heater

Score : $400$ points

Problem Statement

We have a water heater, which supplies $W$ liters of hot water per minute.

There are $N$ people. The $i$-th person plans to use $P_i$ liters of hot water per minute boiled by the heater from Time $S_i$ to $T_i$ (excluding at Time $T_i$ exactly). As hot water gets cold fast, it cannot be stored.

Is it possible to supply hot water to the people according to their plans?

Constraints

• $1\leq N \leq 2\times 10^5$
• $0\leq S_i < T_i \leq 2\times 10^5$
• $1\leq W, P_i \leq 10^9$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $W$

$S_1$ $T_1$ $P_1$

$\vdots$

$S_N$ $T_N$ $P_N$

Output

If it is possible to supply hot water to the people according to their plans, print Yes; otherwise, print No.

4 10
1 3 5
2 4 4
3 10 6
2 4 1

No

Between Time $3$ and $4$, the $2$-nd, $3$-rd, and $4$-th persons plan to use $4$, $6$, and $1$ liter(s) of hot water per minute, for a total of $11$ liters per minute.

The water heater can only supply $10$ liters of hot water per minute, which is not enough.

4 10
1 3 5
2 4 4
3 10 6
2 3 1

Yes

6 1000000000
0 200000 999999999
2 20 1
20 200 1
200 2000 1
2000 20000 1
20000 200000 1

Yes