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.IOException;
import java.io.InputStream;
import java.util.Arrays;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Scanner;


public class Template {

	public static void main(String[] args) throws IOException {
		//Scanner sc = new Scanner(System.in);
		FastReader sc = new FastReader(System.in);	
		int n = sc.nextInt();
		int m = sc.nextInt();
		double min=Double.MAX_VALUE;;
		while(n-- != 0) {
			int a = sc.nextInt();
			int b = sc.nextInt();
			double val = ((double)m) * a;
			double ans = val / b;
			if(ans < min)
				min = ans;
		}
		System.out.println(min);
	
	
	}
}





class FastReader{
    	


        byte[] buf = new byte[2048];
        int index, total;
        InputStream in;

        FastReader(InputStream is) {
            in = is;
        }

        int scan() throws IOException {
            if (index >= total) {
                index = 0;
                total = in.read(buf);
                if (total <= 0) {
                    return -1;
                }
            }
            return buf[index++];
        }

        String next() throws IOException {
            int c;
            for (c = scan(); c <= 32; c = scan()) ;
            StringBuilder sb = new StringBuilder();
            for (; c > 32; c = scan()) {
                sb.append((char) c);
            }
            return sb.toString();
        }

        int nextInt() throws IOException {
            int c, val = 0;
            for (c = scan(); c <= 32; c = scan()) ;
            boolean neg = c == '-';
            if (c == '-' || c == '+') {
                c = scan();
            }
            for (; c >= '0' && c <= '9'; c = scan()) {
                val = (val << 3) + (val << 1) + (c & 15);
            }
            return neg ? -val : val;
        }

        long nextLong() throws IOException {
            int c;
            long val = 0;
            for (c = scan(); c <= 32; c = scan()) ;
            boolean neg = c == '-';
            if (c == '-' || c == '+') {
                c = scan();
            }
            for (; c >= '0' && c <= '9'; c = scan()) {
                val = (val << 3) + (val << 1) + (c & 15);
            }
            return neg ? -val : val;
        }

    	
    }






class Entry implements Comparable<Entry> {
    private int key;
    private int value;

    public Entry(int key, int value) {
        this.key = key;
        this.value = value;
    }

    

    public int first() {
		return key;
	}



	public void setFirst(int key) {
		this.key = key;
	}



	public int second() {
		return value;
	}



	public void setSecond(int value) {
		this.value = value;
	}



	@Override
    public int compareTo(Entry other) {
        if(this.key > other.key)
        	return 1;
        else if(this.key < other.key)
        	return -1;
        else 
        	return 0;
        
    }



	public static Entry add(int i, int j) {
		
		return new Entry(i, j);
	}
}

 class Pair<First, Second> {
    private First first;
    private Second second;

    public Pair(First first, Second second) {
        this.first = first;
        this.second = second;
    }

    public void setFirst(First first) {
        this.first = first;
    }

    public void setSecond(Second second) {
        this.second = second;
    }

    public First getFirst() {
        return first;
    }

    public Second getSecond() {
        return second;
    }

    public void set(First first, Second second) {
        setFirst(first);
        setSecond(second);
    }

    @Override
    public boolean equals(Object o) {
        if (this == o) return true;
        if (o == null || getClass() != o.getClass()) return false;

        Pair pair = (Pair) o;

        if (first != null ? !first.equals(pair.first) : pair.first != null) return false;
        if (second != null ? !second.equals(pair.second) : pair.second != null) return false;

        return true;
    }

    
    
    @Override
    public int hashCode() {
        int result = first != null ? first.hashCode() : 0;
        result = 31 * result + (second != null ? second.hashCode() : 0);
        return result;
    }

    static <L,R> Pair<L,R> add(L left, R right){
        return new Pair<L,R>(left, right);
    }

	
}