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 $a_t\ne b_t$, 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