A11765 | Water Taps

Consider 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 $T$ ?

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.

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 $10^{-6}$ .