Integers 1,2,3,...,n are placed on a circle in the increasing or- der as in the following figure. We want to construct a sequence from these numbers on a circle. Starting with the number 1, we continually go round by picking out each k-th number and send to a sequence queue until all numbers on the circle are ex- hausted. This linearly arranged numbers in the queue are called Jump(n,k) sequence where 1 ≤ n,k. Let us compute Jump(10,2) sequence. The first 5 picked numbers are 2, 4, 6, 8, 10 as shown in the following figure. And 3, 7, 1, 9 and 5 will follow. So we get J ump(10, 2) = [2,4,6,8,10,3,7,1,9,5]. In a similar way, we can get easily Jump(13,3) = [3,6,9,12,2,7,11,4,10,5,1,8,13], Jump(13,10) = [10,7,5,4,6,9,13,8,3,12,1,11,2] and Jump(10,19) = [9,10,3,8,1,6,4,5,7,2]. Jump(10,2) = [2,4,6,8,10,3,7,1,9,5] You write a program to print out the last three numbers of Jump(n,k) for n,k given. For example suppose that n = 10, k = 2, then you should print 1, 9 and 5 on the output file. Note that Jump(1,k) = [1]. Input Your program is to read the input from standard input. The input consists of T test cases. The number of test cases T is given in the first line of the input. Each test case starts with a line containing two integers n and k, where 5 ≤ n ≤ 500, 000 and 2 ≤ k ≤ 500, 000. Output Your program is to write to standard output. Print the last three numbers of Jump(n,k) in the order of the last third, second and the last first. Sample Input 3 10 2 13 10 30000 54321 Sample Output 195 1 11 2 10775 17638 23432