9668: ABC183 —— D - Water Heater
[Creator : ]
Description
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?
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?
Input
Input is given from Standard Input in the following format:
```
$N$ $W$
$S_1$ $T_1$ $P_1$
$\vdots$
$S_N$ $T_N$ $P_N$
```
```
$N$ $W$
$S_1$ $T_1$ $P_1$
$\vdots$
$S_N$ $T_N$ $P_N$
```
Output
If it is possible to supply hot water to the people according to their plans, print `Yes`; otherwise, print `No`.
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.
- $0\leq S_i < T_i \leq 2\times 10^5$
- $1\leq W, P_i \leq 10^9$
- All values in input are integers.
Sample 1 Input
4 10
1 3 5
2 4 4
3 10 6
2 4 1
Sample 1 Output
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.
Sample 2 Input
4 10
1 3 5
2 4 4
3 10 6
2 3 1
Sample 2 Output
Yes
Sample 3 Input
6 1000000000
0 200000 999999999
2 20 1
20 200 1
200 2000 1
2000 20000 1
20000 200000 1
Sample 3 Output
Yes