Water Heater

AtCoder

IDabc183_d

Time2000ms

Memory256MB

Difficulty—

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: $N$ $W$ $S_1$ $T_1$ $P_1$ $\vdots$ $S_N$ $T_N$ $P_N$ [samples]

Samples

Input #1

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.

Input #2

Output #2

Yes

Input #3

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

Output #3

Yes

API Response (JSON)

{
  "problem": {
    "name": "Water Heater",
    "description": {
      "content": "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_",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc183_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have a water heater, which supplies $W$ liters of hot water per minute.\nThere 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_...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments