6938번 - Partitions 다국어

문제

Given a positive integer $k,ドル a partition is a sequence of positive integers in decreasing order whose sum is $k$. For example, $(12),ドル $(2,2,2,2,2,2)$ and $(5,3,2,1,1)$ are all partitions of 12ドル$. Given two distinct partitions, $(a_1,a_2,\dots,a_n)$ and $(b_1,b_2,\dots,b_m),ドル 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 $t \le n$ and $t \le m,ドル 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,ドル 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 $k$ and a positive integer $a,ドル you are to find the $a^{th}$ partition in the list of partitions of $k$ sorted in lexicographical order.

입력

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

출력

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

제한

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