Speedometer Correction

Sheila is a student who drives an old, slow, rusty car that is falling apart. Recently, the needle on her speedometer fell off and she reattached it, but possibly at the wrong angle. As a result, when the speedometer shows a reading s, her true speed is s + c, where c is an unknown constant (which may be negative).

Sheila recorded a journey that consisted of n segments. In the i^th segment she traveled a distance of d_i with her speedometer reading s_i during the entire segment. The total time for the journey was t. Your task is to help Sheila determine the value of c such that

$$\sum_{i=1}^{n} \frac{d_i}{s_i + c} = t$$

It is guaranteed that for each segment the true speed, i.e. s_i + c, is greater than zero.

inputFormat

The first line contains two numbers: an integer n and a real number t, where n represents the number of journey segments and t is the total time taken.

Each of the following n lines contains two real numbers: d_i and s_i, which represent the distance traveled and the speedometer reading for the i^th segment respectively.

It is guaranteed that with the correct c, each s_i + c > 0.

outputFormat

Output the constant c. Your answer is accepted if its absolute or relative error does not exceed 10^-7.

sample

3 10
100 20
150 25
200 30

5.000000000