Interval Running

AtCoder

IDsumitb2019_f

Time2000ms

Memory256MB

Difficulty—

Takahashi and Aoki are training for long-distance races in an infinitely long straight course running from west to east. They start simultaneously at the same point and moves as follows **towards the east**: * Takahashi runs $A_1$ meters per minute for the first $T_1$ minutes, then runs at $A_2$ meters per minute for the subsequent $T_2$ minutes, and alternates between these two modes forever. * Aoki runs $B_1$ meters per minute for the first $T_1$ minutes, then runs at $B_2$ meters per minute for the subsequent $T_2$ minutes, and alternates between these two modes forever. How many times will Takahashi and Aoki meet each other, that is, come to the same point? We do not count the start of the run. If they meet infinitely many times, report that fact. ## Constraints * $1 \leq T_i \leq 100000$ * $1 \leq A_i \leq 10^{10}$ * $1 \leq B_i \leq 10^{10}$ * $A_1 \neq B_1$ * $A_2 \neq B_2$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $T_1$ $T_2$ $A_1$ $A_2$ $B_1$ $B_2$ [samples]

Samples

Input #1

1 2
10 10
12 4

Output #1

1

They will meet just once, $\frac{4}{3}$ minutes after they start, at $\frac{40}{3}$ meters from where they start.

Input #2

100 1
101 101
102 1

Output #2

infinity

They will meet $101, 202, 303, 404, 505, 606, ...$ minutes after they start, that is, they will meet infinitely many times.

Input #3

12000 15700
3390000000 3810000000
5550000000 2130000000

Output #3

113

The values in input may not fit into a $32$\-bit integer type.

API Response (JSON)

{
  "problem": {
    "name": "Interval Running",
    "description": {
      "content": "Takahashi and Aoki are training for long-distance races in an infinitely long straight course running from west to east. They start simultaneously at the same point and moves as follows **towards the ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "sumitb2019_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Takahashi and Aoki are training for long-distance races in an infinitely long straight course running from west to east.\nThey start simultaneously at the same point and moves as follows **towards the ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments