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 PYTHON3):

Solution:
import atexit
import io
import sys
import os

from bisect import *
from collections import *
from fractions import gcd
from fractions import Fraction as fr_
from itertools import *
import math

inf = float('inf')  # sys.maxint in py2
inf_neg = float('-inf')  # sys.maxsize = 9*1e18
range_5 = int(1e5 + 1)
range_6 = int(1e6 + 1)
range_7 = int(1e7 + 1)
range_8 = int(1e8 + 1)
# sys.setrecursionlimit(range_8)

# fast io
_INPUT_LINES = sys.stdin.read().splitlines()
input = iter(_INPUT_LINES).__next__
_OUTPUT_BUFFER = io.StringIO()
sys.stdout = _OUTPUT_BUFFER


@atexit.register
def write():
    sys.__stdout__.write(_OUTPUT_BUFFER.getvalue())


def main():
    # code here
    n, m = map(int,input().split())
    # ll = list(map(int, input().split()))
    ll = []
    for _ in range(n):
    	a, b = map(int, input().split()) 
    	ll.append(a/b)
    # print("{}".format())
    print(min(ll)*m)


if __name__ == '__main__':
    main()