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?

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.

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.

Sample Input 1

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

Sample Output 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.

Sample Input 2

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

Sample Output 2

Yes

Sample Input 3

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

Sample Output 3

Yes

见题面 Input 部分

见题面 Output 部分