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.util.*;
import java.io.*;

public class temp{
	static long mod = (long) Math.pow(10, 9) + 7;

	public static void main(String[] args) throws Exception {

		Scan scn = new Scan();
		Print printer = new Print();

		int n = scn.scanInt();
		int m = scn.scanInt();
		double min = Double.MAX_VALUE;
		while (n-- > 0) {
			int a = scn.scanInt();
			int b = scn.scanInt();
			double tmp = (double) a / b;
			min = Math.min(min, tmp);
		}
		
		double ans = min * m;
		printer.printLine(ans + "");

		printer.close();
	}

	static class Scan {
		private InputStream in;
		private byte[] buf = new byte[1024 * 1024];
		private int index;
		private int total;

		public Scan() {
			in = System.in;
			// try {
			// in = new FileInputStream(new File("/home/ujjwal/test/test"));
			// } catch (Exception ex) {
			//
			// }
		}

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

		public int scanInt() throws IOException {
			int integer = 0;
			int n = scan();
			while (isWhiteSpace(n))
				n = scan();
			int neg = 1;
			if (n == '-') {
				neg = -1;
				n = scan();
			}
			while (!isWhiteSpace(n)) {
				if (n >= '0' && n <= '9') {
					integer *= 10;
					integer += n - '0';
					n = scan();
				} else
					throw new InputMismatchException();
			}
			return neg * integer;
		}

		public long scanLong() throws IOException {
			long integer = 0;
			int n = scan();
			while (isWhiteSpace(n))
				n = scan();
			int neg = 1;
			if (n == '-') {
				neg = -1;
				n = scan();
			}
			while (!isWhiteSpace(n)) {
				if (n >= '0' && n <= '9') {
					integer *= 10;
					integer += n - '0';
					n = scan();
				} else
					throw new InputMismatchException();
			}
			return neg * integer;
		}

		public double scanDouble() throws IOException {
			double doub = 0;
			int n = scan();
			while (isWhiteSpace(n))
				n = scan();
			int neg = 1;
			if (n == '-') {
				neg = -1;
				n = scan();
			}
			while (!isWhiteSpace(n) && n != '.') {
				if (n >= '0' && n <= '9') {
					doub *= 10;
					doub += n - '0';
					n = scan();
				} else
					throw new InputMismatchException();
			}
			if (n == '.') {
				n = scan();
				double temp = 1;
				while (!isWhiteSpace(n)) {
					if (n >= '0' && n <= '9') {
						temp /= 10;
						doub += (n - '0') * temp;
						n = scan();
					} else
						throw new InputMismatchException();
				}
			}
			return doub * neg;
		}

		public String scanString() throws IOException {
			StringBuilder sb = new StringBuilder();
			int n = scan();
			while (isWhiteSpace(n))
				n = scan();
			while (!isWhiteSpace(n)) {
				sb.append((char) n);
				n = scan();
			}
			return sb.toString();
		}

		private boolean isWhiteSpace(int n) {
			if (n == ' ' || n == '\n' || n == '\r' || n == '\t' || n == -1)
				return true;
			return false;
		}
	}

	static class Print {
		private final BufferedWriter bw;

		public Print() {
			bw = new BufferedWriter(new OutputStreamWriter(System.out));
		}

		public void print(String str) throws IOException {
			bw.append(str);
		}

		public void printLine(String str) throws IOException {
			print(str);
			bw.append("\n");
		}

		public void close() throws IOException {
			bw.close();
		}
	}

}