CF670D2.Magic Powder - 2

The term of this problem is the same as the previous one, the only exception — increased restrictions.

The first line contains two positive integers $n$ and $k$ ( $1<=n<=100000,1<=k<=10^{9}$ ) — the number of ingredients and the number of grams of the magic powder.

The second line contains the sequence $a_{1},a_{2},...,a_{n}$ ( $1<=a_{i}<=10^{9}$ ), where the $i$ -th number is equal to the number of grams of the $i$ -th ingredient, needed to bake one cookie.

The third line contains the sequence $b_{1},b_{2},...,b_{n}$ ( $1<=b_{i}<=10^{9}$ ), where the $i$ -th number is equal to the number of grams of the $i$ -th ingredient, which Apollinaria has.

Print the maximum number of cookies, which Apollinaria will be able to bake using the ingredients that she has and the magic powder.

In the first sample it is profitably for Apollinaria to make the existing $1$ gram of her magic powder to ingredient with the index $2$ , then Apollinaria will be able to bake $4$ cookies.

In the second sample Apollinaria should turn $1$ gram of magic powder to ingredient with the index $1$ and $1$ gram of magic powder to ingredient with the index $3$ . Then Apollinaria will be able to bake $3$ cookies. The remaining $1$ gram of the magic powder can be left, because it can't be used to increase the answer.