Contest Duration: - (local time) (100 minutes) Back to Home
D - Water Heater /

Time Limit: 2 sec / Memory Limit: 1024 MB

### 問題文

N 人の人がいます。i 番目の人は時刻 S_i から T_i までの間 (時刻 T_i ちょうどを除く)、この湯沸かし器で沸かしたお湯を毎分 P_i リットル使おうと計画しています。お湯はすぐ冷めてしまうので、溜めておくことはできません。

すべての人に計画通りにお湯を供給することはできますか？

### 制約

• 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
• 入力はすべて整数

### 入力

N W
S_1 T_1 P_1
\vdots
S_N T_N P_N


### 出力

すべての人に計画通りにお湯を供給することができるなら Yesを、できないなら Noを出力せよ。

### 入力例 1

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


### 出力例 1

No


### 入力例 2

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


### 出力例 2

Yes


### 入力例 3

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


### 出力例 3

Yes


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.

### 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