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A. Supermarket

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputWe 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.

Input

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.

Output

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 $$$\frac{|x - y|}{\max{(1, |y|)}} \le 10^{-6}$$$.

Examples

Input

3 5

1 2

3 4

1 3

Output

1.66666667

Input

2 1

99 100

98 99

Output

0.98989899

Note

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.

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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