Bus Stops

AtCoder

IDabc319_e

Time3000ms

Memory256MB

Difficulty—

Takahashi is initially at his house and is about to visit Aoki's house. There are $N$ bus stops numbered $1$ to $N$ between the two houses, and Takahashi can move between them in the following ways: * He can walk from his house to bus stop $1$ in $X$ units of time. * For each $i = 1, 2, \ldots, N-1$, a bus departs from bus stop $i$ at each time that is a multiple of $P_i$, and by taking this bus, he can get to bus stop $(i+1)$ in $T_i$ units of time. **Here, the constraints guarantee that $1 \leq P_i \leq 8$.** * Takahashi can walk from bus stop $N$ to Aoki's house in $Y$ units of time. For each $i = 1, 2, \ldots, Q$, process the following query. > Find the earliest time that Takahashi can arrive at Aoki's house when he leaves his house at time $q_i$. Note that if he arrives at a bus stop exactly at the departure time of a bus, he can take that bus. ## Constraints * $2 \leq N \leq 10^5$ * $1 \leq X, Y \leq 10^9$ * $1 \leq P_i \leq 8$ * $1 \leq T_i \leq 10^9$ * $1 \leq Q \leq 2 \times 10^5$ * $0 \leq q_i \leq 10^9$ * All input values are integers. ## Input The input is given from Standard Input in the following format: $N$ $X$ $Y$ $P_1$ $T_1$ $P_2$ $T_2$ $\vdots$ $P_{N-1}$ $T_{N-1}$ $Q$ $q_1$ $q_2$ $\vdots$ $q_Q$ [samples]

Samples

Input #1

Output #1

34
22
710511052
136397548
763027402
644706946
447672250

For the first query, Takahashi can move as follows to arrive at Aoki's house at time $34$.

*   Leave his house at time $13$.
*   Walk from his house and arrive at bus stop $1$ at time $15$.
*   Take the bus departing from bus stop $1$ at time $15$ and arrive at bus stop $2$ at time $19$.
*   Take the bus departing from bus stop $2$ at time $24$ and arrive at bus stop $3$ at time $30$.
*   Take the bus departing from bus stop $3$ at time $30$ and arrive at bus stop $4$ at time $31$.
*   Walk from bus stop $4$ and arrive at Aoki's house at time $34$.

For the second query, Takahashi can move as follows and arrive at Aoki's house at time $22$.

*   Leave his house at time $0$.
*   Walk from his house and arrive at bus stop $1$ at time $2$.
*   Take the bus departing from bus stop $1$ at time $5$ and arrive at bus stop $2$ at time $9$.
*   Take the bus departing from bus stop $2$ at time $12$ and arrive at bus stop $3$ at time $18$.
*   Take the bus departing from bus stop $3$ at time $18$ and arrive at bus stop $4$ at time $19$.
*   Walk from bus stop $4$ and arrive at Aoki's house at time $22$.

API Response (JSON)

{
  "problem": {
    "name": "Bus Stops",
    "description": {
      "content": "Takahashi is initially at his house and is about to visit Aoki's house. There are $N$ bus stops numbered $1$ to $N$ between the two houses, and Takahashi can move between them in the following ways: ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 3000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc319_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Takahashi is initially at his house and is about to visit Aoki's house.\nThere are $N$ bus stops numbered $1$ to $N$ between the two houses, and Takahashi can move between them in the following ways:\n\n...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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