You are given two integers l and r.
You have to choose k real numbers in the interval [l,r]
uniform randomly.
What is the expected count of distinct numbers chosen by you?
Input
The first line of the input contains a single integer T
denoting the number of test cases. The description of T
test cases follows.
The first and only line of each test case contains three space-separated integers l
, r and k
.
Output
For each test case, print a single line containing one integer - the expected count of distinct numbers chosen. It can be proved that the expected count is always an integer.
Constraints
1≤T≤105
1≤k≤100
1≤l≤r≤100
Example Input
3
3 6 4
1 3 1
6 7 2
Example Output
4
1
2
Explanation
Example case 2: You choose only 1
real number, so it doesn’t matter which real number you chose, number of distinct number is always 1. So expected count of distinct number is 1.
