Sheila made a careful record of a recent journey and wants to use this to compute $c$. The journey consisted of $n$ segments. In the $i^{\text {th}}$ segment she traveled a distance of $d_ i$ and the speedometer read $s_ i$ for the entire segment. This whole journey took time $t$. Help Sheila by computing $c$.
Note that while Sheila’s speedometer might have negative readings, her true speed was greater than zero for each segment of the journey.
The first line of input contains two integers $n$ ($1 \le n \le 1\, 000$), the number of sections in Sheila’s journey, and $t$ ($1 \le t \le 10^6$), the total time. This is followed by $n$ lines, each describing one segment of Sheila’s journey. The $i^{\text {th}}$ of these lines contains two integers $d_ i$ ($1 \le d_ i \le 1\, 000$) and $s_ i$ ($|s_ i| \le 1\, 000$), the distance and speedometer reading for the $i^{\text {th}}$ segment of the journey. Time is specified in hours, distance in miles, and speed in miles per hour.
Display the constant $c$ in miles per hour. Your answer should have an absolute or relative error of less than $10^{-6}$.
Sample Input 1 | Sample Output 1 |
---|---|
3 5 4 -1 4 0 10 3 |
3.000000000 |
Sample Input 2 | Sample Output 2 |
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4 10 5 3 2 2 3 6 3 1 |
-0.508653377 |