Problem: You are given three integers A,B and C.
 We choose two real numbers x and y such that 0 ≤ x ≤ A and 0 ≤ y ≤ B.
 What is the probability that x+y≤C ?


Input
The first line of input contains T denoting the number of test cases.
Each of the following T lines contains three space separated Integers A,B and C

Output
For each test case, output a single line containing the required probablity.

Constraints
1 ≤ T ≤ 10^5 
0 ≤ A,B ≤ 10^9 
0 ≤ C ≤ 10^18 

Example
Input:

2
4 10 3
4 10 11


Output:

0.1125
0.8875


NOTE: Your answer will be accepted if the absolute error is less than 10^-6.

Solution (in PYTHON):

Solution:
t = int(input())
for i in range(t):
    a,b,c = map(float, raw_input().split())
    ans = 0.0
    if(a==0 and b ==0):
        ans = 1

    elif (a==0 and b!=0):

        if (c>=b):
            ans = 1.0
        else:
            ans = c/b

    elif (a!=0 and b==0):

        if(c>=a):
            ans = 1.0
        else:
            ans = c/a

    elif (c<=a and c<=b):

        ans = ((c/a)*(c/b))/2

    elif (b<= c and c<a):

        ans = (c/(2*a))*(c/b)-((c-b)/(2*a))*(c-b)/b

    elif (a<=c and c<b):

        ans = (c/(2*a))*(c/b)-((c-a)/(2*a))*((c-a)/b)

    elif (c > a and c > b and c<=(a+b)):

        ans = (c/(2*a))*(c/b)-((c-a)/(2*a))*((c-a)/b)-((c-b)/(2*a))*((c-b)/b)

    elif c>(a+b):

        ans = 1

    print ans