Special Trains

AtCoder

IDabc084_c

Time3000ms

Memory256MB

Difficulty—

A railroad running from west to east in Atcoder Kingdom is now complete. There are $N$ stations on the railroad, numbered $1$ through $N$ from west to east. Tomorrow, the opening ceremony of the railroad will take place. On this railroad, for each integer $i$ such that $1≤i≤N-1$, there will be trains that run from Station $i$ to Station $i+1$ in $C_i$ seconds. No other trains will be operated. The first train from Station $i$ to Station $i+1$ will depart Station $i$ $S_i$ seconds after the ceremony begins. Thereafter, there will be a train that departs Station $i$ every $F_i$ seconds. Here, it is guaranteed that $F_i$ divides $S_i$. That is, for each Time $t$ satisfying $S_i≤t$ and $t％F_i=0$, there will be a train that departs Station $i$ $t$ seconds after the ceremony begins and arrives at Station $i+1$ $t+C_i$ seconds after the ceremony begins, where $A％B$ denotes $A$ modulo $B$, and there will be no other trains. For each $i$, find the earliest possible time we can reach Station $N$ if we are at Station $i$ when the ceremony begins, ignoring the time needed to change trains. ## Constraints * $1≤N≤500$ * $1≤C_i≤100$ * $1≤S_i≤10^5$ * $1≤F_i≤10$ * $S_i％F_i=0$ * All input values are integers. ## Input Input is given from Standard Input in the following format: $N$ $C_1$ $S_1$ $F_1$ $:$ $C_{N-1}$ $S_{N-1}$ $F_{N-1}$ [samples]

Samples

Input #1

3
6 5 1
1 10 1

Output #1

12
11
0

We will travel from Station $1$ as follows:

*   $5$ seconds after the beginning: take the train to Station $2$.
*   $11$ seconds: arrive at Station $2$.
*   $11$ seconds: take the train to Station $3$.
*   $12$ seconds: arrive at Station $3$.

We will travel from Station $2$ as follows:

*   $10$ seconds: take the train to Station $3$.
*   $11$ seconds: arrive at Station $3$.

Note that we should print $0$ for Station $3$.

Input #2

Output #2

Input #3

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Special Trains",
    "description": {
      "content": "A railroad running from west to east in Atcoder Kingdom is now complete. There are $N$ stations on the railroad, numbered $1$ through $N$ from west to east. Tomorrow, the opening ceremony of the railr",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 3000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc084_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "A railroad running from west to east in Atcoder Kingdom is now complete.\nThere are $N$ stations on the railroad, numbered $1$ through $N$ from west to east.\nTomorrow, the opening ceremony of the railr...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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