Fishing

AtCoder

IDabc274_f

Time3000ms

Memory256MB

Difficulty—

On a number line, there are $N$ fish swimming. Fish $i$, which has a weight of $W_i$, is at the coordinate $X_i$ at time $0$ and moves at a speed of $V_i$ in the positive direction. Takahashi will choose an arbitrary real number $t$ greater than or equal to $0$ and do the following action at time $t$ just once. Action: Choose an arbitrary real number $x$. Catch all fish whose coordinates are between $x$ and $x+A$, inclusive. Find the maximum total weight of fish that he can catch. ## Constraints * $1 \leq N \leq 2000$ * $1 \leq A \leq 10^4$ * $1 \leq W_i\leq 10^4$ * $0 \leq X_i\leq 10^4$ * $1 \leq V_i\leq 10^4$ * All values in the input are integers. ## Input The input is given from Standard Input in the following format: $N$ $A$ $W_1$ $X_1$ $V_1$ $W_2$ $X_2$ $V_2$ $\vdots$ $W_N$ $X_N$ $V_N$ [samples]

Samples

Input #1

Output #1

111

At time $0.25$, fish $1$, $2$, and $3$ are at the coordinates $25$, $17.5$, and $22.5$, respectively. Thus, the action done at this time with $x=16$ catches all the fish.

Input #2

3 10
100 100 100
1 10 30
10 20 10

Output #2

100

One optimal choice is to do the action at time $0$ with $x=100$.

Input #3

4 10
1000 100 10
100 99 1
10 0 100
1 1 1

Output #3

1110

One optimal choice is to do the action at time $1$ with $x=100$.

API Response (JSON)

{
  "problem": {
    "name": "Fishing",
    "description": {
      "content": "On a number line, there are $N$ fish swimming. Fish $i$, which has a weight of $W_i$, is at the coordinate $X_i$ at time $0$ and moves at a speed of $V_i$ in the positive direction. Takahashi will cho",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 3000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc274_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "On a number line, there are $N$ fish swimming.\nFish $i$, which has a weight of $W_i$, is at the coordinate $X_i$ at time $0$ and moves at a speed of $V_i$ in the positive direction.\nTakahashi will cho...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments