Problem: 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.

Input

The first line contains two positive integers n and m (1 ≤ n ≤ 5 000, 1 ≤ m ≤ 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 ≤ a, b ≤ 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|)}} ≤ 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.

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.StringTokenizer;

public class A {

    static BufferedReader sc;
    static PrintWriter w;
    static StringTokenizer st;

    public static void main(String[] args) throws IOException {
        sc = new BufferedReader(new InputStreamReader(System.in));
        w = new PrintWriter(System.out);

        // sc = new BufferedReader(new FileReader("input.txt"));
        // w = new PrintWriter(new FileWriter("output.txt"));

        st = new StringTokenizer(sc.readLine());

        start();

        w.close();
        sc.close();
    }

    private static void start() throws IOException {
        int n = nextInt();
        int m = nextInt();
        
        double min = Double.MAX_VALUE;

        for (int i = 0; i < n; i++) {
            int a = nextInt();
            int b = nextInt();

            double d = (double) a / b;

            if(d < min) min = d;
        }

        w.println(m*min);
    }

    public static String nextToken() throws IOException {
        if (!st.hasMoreTokens())
            st = new StringTokenizer(sc.readLine());
        return st.nextToken();
    }

    public static int nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }

    public static double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }

    public static double nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }

    public static String next() throws IOException {
        return nextToken();
    }

    public static String nextLine() throws IOException {
        String s = sc.readLine();
        return s;
    }
}