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 PYTHON3):

Solution:
#   ==========     //\\       //||     ||====//||
#       ||        //  \\        ||     ||   // ||
#       ||       //====\\       ||     ||  //  ||
#       ||      //      \\      ||     || //   ||
#   ========== //        \\  ========  ||//====|| 
#  code

def solve():
    a,b,c,d = map(int, input().split())

    p = a / b
    q = c / d

    ans = p * (1  / (1 - (1 - p) * (1 - q)))
    print(ans)
    return

def main():
    t = 1
    # t = int(input())
    for _ in range(t):
        solve()

if __name__ == "__main__":
    main()