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.math.BigInteger;
	import java.util.*;
import java.util.Map.Entry;

	
	public class Main
	{
		private InputStream stream;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;
		private SpaceCharFilter filter;
		private PrintWriter pw;
		private long mod = 1000000000 + 7;
		
		private StringBuilder ans_sb;
		private int block;
		private long[] masks;
		private void soln()
		{
			int n = nextInt();
			double m = nextInt();
			double min = Integer.MAX_VALUE;
			for(int i=0;i<n;i++) {
				double x = nextInt();
				double y = nextInt();
				min = Math.min(min, x/y);
			}
			pw.println(min*m);
		}
		private String solveEqn(long a, long b) {
	        long x = 0, y = 1, lastx = 1, lasty = 0, temp;
	        while (b != 0){
	        	long q = a / b;
	        	long r = a % b;
	            a = b;
	            b = r;
	            temp = x;
	            x = lastx - q * x;
	            lastx = temp;
	            temp = y;
	            y = lasty - q * y;
	            lasty = temp;
	        }
	        return lastx+" "+lasty;
		}
		private void debug(Object... o) {
			System.out.println(Arrays.deepToString(o));
		}
		
		private long pow(long a, long b, long c)
		{
			if (b == 0)
				return 1;
			long p = pow(a, b / 2, c);
			p = (p * p) % c;
			return (b % 2 == 0) ? p : (a * p) % c;
		}
	
		private long gcd(long n, long l)
		{
			if (l == 0)
				return n;
			return gcd(l, n % l);
		}
		public static void main(String[] args) throws Exception
		{
			/*new Thread(null, new Runnable()
			{
				@Override
				public void run()
				{
					new Main().solve();
				}
			}, "1", 1 << 25).start();*/
			new Main().solve();
		}
		public StringBuilder solve(){
			InputReader(System.in);
			/*try { 
				InputReader(new FileInputStream("C:\\Users\\hardik\\Desktop\\in.txt"));
			} catch(FileNotFoundException e) {}
			*/
			pw = new PrintWriter(System.out);
			//ans_sb = new StringBuilder();
			soln();
			
			pw.close();
			//System.out.println(ans_sb);
			return ans_sb;
		}
		public void InputReader(InputStream stream1)
		{
			stream = stream1;
		}
	
		private boolean isWhitespace(int c)
		{
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}
	
		private boolean isEndOfLine(int c)
		{
			return c == '\n' || c == '\r' || c == -1;
		}
	
		private int read()
		{
			if (numChars == -1)
				throw new InputMismatchException();
			if (curChar >= numChars)
			{
				curChar = 0;
				try
				{
					numChars = stream.read(buf);
				} catch (IOException e)
				{
					throw new InputMismatchException();
				}
				if (numChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}
	
		private int nextInt()
		{
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-')
			{
				sgn = -1;
				c = read();
			}
			int res = 0;
			do
			{
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}
	
		private long nextLong()
		{
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-')
			{
				sgn = -1;
				c = read();
			}
			long res = 0;
			do
			{
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}
	
		private String nextToken()
		{
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do
			{
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}
	
		private String nextLine()
		{
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do
			{
				res.appendCodePoint(c);
				c = read();
			} while (!isEndOfLine(c));
			return res.toString();
		}
	
		private int[] nextIntArray(int n)
		{
			int[] arr = new int[n];
			for (int i = 0; i < n; i++)
			{
				arr[i] = nextInt();
			}
			return arr;
		}
	
		private long[] nextLongArray(int n)
		{
			long[] arr = new long[n];
			for (int i = 0; i < n; i++)
			{
				arr[i] = nextLong();
			}
			return arr;
		}
	
		private void pArray(int[] arr)
		{
			for (int i = 0; i < arr.length; i++)
			{
				System.out.print(arr[i] + " ");
			}
			System.out.println();
			return;
		}
	
		private void pArray(long[] arr)
		{
			for (int i = 0; i < arr.length; i++)
			{
				System.out.print(arr[i] + " ");
			}
			System.out.println();
			return;
		}
	
		private boolean isSpaceChar(int c)
		{
			if (filter != null)
				return filter.isSpaceChar(c);
			return isWhitespace(c);
		}
	
		private char nextChar()
		{
			int c = read();
			while (isSpaceChar(c))
				c = read();
			char c1 = (char) c;
			while (!isSpaceChar(c))
				c = read();
			return c1;
		}
	
		private interface SpaceCharFilter
		{
			public boolean isSpaceChar(int ch);
		}
	}