Preparando MOJI
We often go to supermarkets to buy some fruits or vegetables, and on the tag there prints the price for a kilo. But in some supermarkets, when asked how much the items are, the clerk will say that $$$a$$$ yuan for $$$b$$$ kilos (You don't need to care about what "yuan" is), the same as $$$a/b$$$ yuan for a kilo.
Now imagine you'd like to buy $$$m$$$ kilos of apples. You've asked $$$n$$$ supermarkets and got the prices. Find the minimum cost for those apples.
You can assume that there are enough apples in all supermarkets.
The first line contains two positive integers $$$n$$$ and $$$m$$$ ($$$1 \leq n \leq 5\,000$$$, $$$1 \leq m \leq 100$$$), denoting that there are $$$n$$$ supermarkets and you want to buy $$$m$$$ kilos of apples.
The following $$$n$$$ lines describe the information of the supermarkets. Each line contains two positive integers $$$a, b$$$ ($$$1 \leq a, b \leq 100$$$), denoting that in this supermarket, you are supposed to pay $$$a$$$ yuan for $$$b$$$ kilos of apples.
The only line, denoting the minimum cost for $$$m$$$ kilos of apples. Please make sure that the absolute or relative error between your answer and the correct answer won't exceed $$$10^{-6}$$$.
Formally, let your answer be $$$x$$$, and the jury's answer be $$$y$$$. Your answer is considered correct if $$$\frac{|x - y|}{\max{(1, |y|)}} \le 10^{-6}$$$.
3 5
1 2
3 4
1 3
1.66666667
2 1
99 100
98 99
0.98989899
In the first sample, you are supposed to buy $$$5$$$ kilos of apples in supermarket $$$3$$$. The cost is $$$5/3$$$ yuan.
In the second sample, you are supposed to buy $$$1$$$ kilo of apples in supermarket $$$2$$$. The cost is $$$98/99$$$ yuan.