Problem: SmallR is an archer. SmallR is taking a match of archer with Zanoes. They try to shoot in the target in turns, and SmallR shoots first. The probability of shooting the target each time is <image> for SmallR while <image> for Zanoes. The one who shoots in the target first should be the winner.

Output the probability that SmallR will win the match.

Input

A single line contains four integers <image>.

Output

Print a single real number, the probability that SmallR will win the match.

The answer will be considered correct if the absolute or relative error doesn't exceed 10 - 6.

Examples

Input

1 2 1 2


Output

0.666666666667

Solution (in PYTHON):

Solution:
#!/usr/bin/env python
# -*- coding: UTF-8 -*-

import sys

if __name__ == '__main__':
    a, b, c, d = [int(x) for x in raw_input().split()]
    print (1.0 * a / b) / (1.0 - (1.0 * (b - a) / b) * (1.0 * (d - c) / d))