409226: GYM103463 F Hsueh- Love Matrix
Description
Hsueh- constructed a matrix of $$$n$$$ rows and $$$m$$$ columns, the label starts from $$$1$$$. He makes the element in the $$$i$$$-th row and $$$j$$$-th column $$$a_{i, j}$$$ equal to $$$i$$$ times $$$j$$$. i.e. $$$a_{i, j} = i \cdot j$$$. You need to find the $$$k$$$-th largest element.
Unfortunately, Hsueh- only has ten fingers, so he can't count numbers with more than ten digits. Therefore, if the answer is strictly greater than $$$9,999,999,999$$$, just output "Oops"(without quotes).
For instance, we consider $$$n = 2$$$ and $$$m = 3$$$, The matrix elements are as follows:
$$$$$$ \left[ \begin{array}{ccc} 1&2&3\\ 2&4&6 \end{array} \right] $$$$$$
- $$$k = 1$$$, the answer is $$$6$$$.
- $$$k = 2$$$, the answer is $$$4$$$.
- $$$k = 3$$$, the answer is $$$3$$$.
- $$$k = 4$$$, the answer is $$$2$$$.
- $$$k = 5$$$, the answer is $$$2$$$.
- $$$k = 6$$$, the answer is $$$1$$$.
There are several test cases.
The first line contains a single integer $$$T(1 \leq T \leq 5)$$$, denoting the number of test cases. Then follow all the test cases.
For each test case, The first line contains three integers $$$n, m(1 \leq n, m \leq 10^9)$$$ and $$$k(1 \leq k \leq n \cdot m)$$$, representing you need to find the $$$k$$$-th largest element in $$$n$$$ rows and $$$m$$$ columns matrix.
OutputFor each test case, output in one line "Oops"(without quotes) if the answer strictly greater than $$$9,999,999,999$$$, or print a single integer in one line: the $$$k$$$-th largest element of the matrix.
ExamplesInput5 1 1 1 2 3 6 3 3 2 1 10 10 100 100 100Output
1 1 6 1 8722Input
1 1000000000 1000000000 1Output
Oops