Contest Duration: - (local time) (100 minutes) Back to Home
F - Interval Running /

Time Limit: 2 sec / Memory Limit: 1024 MB

### 問題文

• 高橋君は最初の T_1 分間、分速 A_1 メートルで走り、次の T_2 分間、分速 A_2 メートルで走り、これを交互にいつまでも繰り返す。
• 青木君は最初の T_1 分間、分速 B_1 メートルで走り、次の T_2 分間、分速 B_2 メートルで走り、これを交互にいつまでも繰り返す。

さて、高橋君と青木君は何回出会う、すなわち、同じ位置に来るでしょうか？スタート地点にいる時は数えません。無限回出会う場合は、その旨を報告してください。

### 制約

• 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
• 入力中の値はすべて整数

T_1 T_2
A_1 A_2
B_1 B_2

### 出力

ただし、無限回出会う場合は代わりに infinity と出力してください。

1 2
10 10
12 4

1

100 1
101 101
102 1

infinity

### 入力例 3

12000 15700
3390000000 3810000000
5550000000 2130000000

### 出力例 3

113

Score: 600 points

### Problem Statement

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

### Output

Print the number of times Takahashi and Aoki will meet each other.
If they meet infinitely many times, print infinity instead.

1 2
10 10
12 4

### Sample Output 1

1

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

100 1
101 101
102 1

### Sample Output 2

infinity

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

### Sample Input 3

12000 15700
3390000000 3810000000
5550000000 2130000000

### Sample Output 3

113

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