Oversleeping

AtCoder

IDabc193_e

Time2000ms

Memory256MB

Difficulty—

A train goes back and forth between Town $A$ and Town $B$. It departs Town $A$ at time $0$ and then repeats the following: * goes to Town $B$, taking $X$ seconds; * stops at Town $B$ for $Y$ seconds; * goes to Town $A$, taking $X$ seconds; * stops at Town $A$ for $Y$ seconds. More formally, these intervals of time are half-open, that is, for each $n = 0, 1, 2, \dots$: * at time $t$ such that $(2X + 2Y)n ≤ t < (2X + 2Y)n + X$, the train is going to Town $B$; * at time $t$ such that $(2X + 2Y)n + X ≤ t < (2X + 2Y)n + X + Y$, the train is stopping at Town $B$; * at time $t$ such that $(2X + 2Y)n + X + Y ≤ t < (2X + 2Y)n + 2X + Y$, the train is going to Town $A$; * at time $t$ such that $(2X + 2Y)n + 2X + Y ≤ t < (2X + 2Y)(n + 1)$, the train is stopping at Town $A$. Takahashi is thinking of taking this train to depart Town $A$ at time $0$ and getting off at Town $B$. After the departure, he will repeat the following: * be asleep for $P$ seconds; * be awake for $Q$ seconds. Again, these intervals of time are half-open, that is, for each $n = 0, 1, 2, \dots$: * at time $t$ such that $(P + Q)n ≤ t < (P + Q)n + P$, Takahashi is asleep; * at time $t$ such that $(P + Q)n + P ≤ t < (P + Q)(n + 1)$, Takahashi is awake. He can get off the train at Town $B$ if it is stopping at Town $B$ and he is awake. Determine whether he can get off at Town $B$. If he can, find the earliest possible time to do so. Under the constraints of this problem, it can be proved that the earliest time is an integer. You are given $T$ cases. Solve each of them. ## Constraints * All values in input are integers. * $1 ≤ T ≤ 10$ * $1 ≤ X ≤ 10^9$ * $1 ≤ Y ≤ 500$ * $1 ≤ P ≤ 10^9$ * $1 ≤ Q ≤ 500$ ## Input Input is given from Standard Input in the following format: $T$ $\rm case_1$ $\rm case_2$ $\hspace{9pt}\vdots$ $\rm case_T$ Each case is in the following format: $X$ $Y$ $P$ $Q$ [samples]

Samples

Input #1

3
5 2 7 6
1 1 3 1
999999999 1 1000000000 1

Output #1

20
infinity
1000000000999999999

Let $[a, b)$ denote the interval $a ≤ t < b$.
In the first case, the train stops at Town $B$ during $[5, 7), [19, 21), [33, 35), \dots$, and Takahashi is awake during $[7, 13), [20, 26), [33, 39), \dots$, so he can get off at time $20$ at the earliest.

API Response (JSON)

{
  "problem": {
    "name": "Oversleeping",
    "description": {
      "content": "A train goes back and forth between Town $A$ and Town $B$. It departs Town $A$ at time $0$ and then repeats the following: *   goes to Town $B$, taking $X$ seconds; *   stops at Town $B$ for $Y$ seco",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc193_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "A train goes back and forth between Town $A$ and Town $B$. It departs Town $A$ at time $0$ and then repeats the following:\n\n*   goes to Town $B$, taking $X$ seconds;\n*   stops at Town $B$ for $Y$ seco...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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