HOD of CSE Dept. of MMMEC, asked the students to form the groups for their final year project. He said that there will be t students per team and there will be at least 4 boys and at least 1 girl per group.

A curious student Rajesh want to know the total number of ways by which the groups can be made. Because he is busy in forming his group so you, write a program to find the total ways and help him.

Input

First line contains an integer n which itself indicates number of test cases.

Each test case comprises of three space separated integers "B G t". Where B denotes number of boys, G denotes number of girls in the class, and t denotes number of students in a group.

Constraints

1 <= n <= 20

4 <= B <= 30

1 <= G <= 30

5 <= t <= B + G

Output

For each test case print total number of ways per line.

Example

Input:
2
4 1 5
30 30 20

Output:
1
4191318957352590