Canadian Computing Competition: 2001 Stage 2, Day 1, Problem 3

Given a positive integer ~k~, a partition is a sequence of positive integers in decreasing order whose sum is ~k~. For example, ~(12)~, ~(2,2,2,2,2,2)~ and ~(5,3,2,1,1)~ are all partitions of ~12~. Given two distinct partitions, ~(a_1,a_2,\dots,a_n)~ and ~(b_1,b_2,\dots,b_m)~, we will say that ~(a_1,a_2,\dots,a_n) > (b_1,b_2,\dots,b_m)~ if, for the smallest positive integer ~t~ such that ~a_t \neq b_t~, we have ~a_t > b_t~.

This ordering lets us put all the partitions of a given integer ~k~ in lexicographical order, where each partition in the ordering is greater than all the partitions before it.

For example, if ~k = 5~, the partitions in lexicographical order are

(1,1,1,1,1)
(2,1,1,1)
(2,2,1)
(3,1,1)
(3,2)
(4,1)
(5)

Given ~k~ ~(1 \le k \le 100)~ and a positive integer ~a~ ~(1 \le a \le 2 \times 10^9)~, you are to find the ~a^{th}~ partition in the list of partitions of ~k~ sorted in lexicographical order.

Input Specification

The input will consist of a line with ~N~, the number of test cases, followed by ~N~ lines, each of the form ~k~ ~a~, where ~k~ and ~a~ are positive integers.

Output Specification

For each test case, your program should output the ~a^{th}~ partition in the list of partitions of ~k~, or, if ~a~ is greater than the number of partitions of ~k~, output Too big.

Sample Input

3
1 1
5 4
5 8

Sample Output

(1)
(3,1,1)
Too big