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E. Water Taps

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputConsider a system of *n* water taps all pouring water into the same container. The *i*-th water tap can be set to deliver any amount of water from 0 to *a*_{i} ml per second (this amount may be a real number). The water delivered by *i*-th tap has temperature *t*_{i}.

If for every you set *i*-th tap to deliver exactly *x*_{i} ml of water per second, then the resulting temperature of water will be (if , then to avoid division by zero we state that the resulting water temperature is 0).

You have to set all the water taps in such a way that the resulting temperature is exactly *T*. What is the maximum amount of water you may get per second if its temperature has to be *T*?

Input

The first line contains two integers *n* and *T* (1 ≤ *n* ≤ 200000, 1 ≤ *T* ≤ 10^{6}) — the number of water taps and the desired temperature of water, respectively.

The second line contains *n* integers *a*_{1}, *a*_{2}, ..., *a*_{n} (1 ≤ *a*_{i} ≤ 10^{6}) where *a*_{i} is the maximum amount of water *i*-th tap can deliver per second.

The third line contains *n* integers *t*_{1}, *t*_{2}, ..., *t*_{n} (1 ≤ *t*_{i} ≤ 10^{6}) — the temperature of water each tap delivers.

Output

Print the maximum possible amount of water with temperature exactly *T* you can get per second (if it is impossible to obtain water with such temperature, then the answer is considered to be 0).

Your answer is considered correct if its absolute or relative error doesn't exceed 10^{ - 6}.

Examples

Input

2 100

3 10

50 150

Output

6.000000000000000

Input

3 9

5 5 30

6 6 10

Output

40.000000000000000

Input

2 12

1 3

10 15

Output

1.666666666666667

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

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