N friends are playing a game of truth and dare. They sit in a circle and then person numbered k rotates the bottle that point himself first. Now bottle points a total of exactly p people and stops. If p is even then the outcome is truth or else dare. You are given t test cases each with three values N,K and p.You have to provide the number of the person on which the bottle will stop and what is the outcome for each of the test case.
Please note that p is the total people to whom bottle points at including the one who is rotating. Also if p>n then it means that bottle has visited the same person more than once
For example suppose bottle is pointing initially person numbered 1 and now he rotates the bottle and suppose value of p is 3 then it means that bottle stops at the person numbered 3
Input
First line contains total testcases t as input. Next t lines contain three integers N,K and p meaning explained in the statement
Output:
For each test case, print the number of person to which the bottle will point, and also the outcome("truth" or "dare") separated by space.
Constraints
1<= t <=100000
1<= N <=10^18
1<= K <=10^18
1<= p <=10^18
After 5 motions i.e 5 6 7 8 1 it stops at 1, and as p is odd the case is dare