Pinely Round 3 (Div. 1 + Div. 2) |
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Finished |
There are $$$n$$$ positive integers $$$a_1, a_2, \dots, a_n$$$ on a blackboard. You are also given a positive integer $$$k$$$. You can perform the following operation some (possibly $$$0$$$) times:
Is it possible to make all the numbers on the blackboard equal? If yes, what is the minimum number of operations you need?
Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^4$$$). The description of the test cases follows.
The first line of each test case contains two integers $$$n$$$, $$$k$$$ ($$$1 \le n \le 2 \cdot 10^5$$$, $$$1 \leq k \leq 10^{12}$$$) — the number of integers initially on the blackboard and the constant $$$k$$$.
The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \le a_i \le 10^{12}$$$) — the initial state of the blackboard.
It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.
For each test case, output a single line containing an integer: the minimum number of operations you need to make all the numbers on the blackboard equal, or $$$-1$$$ if it is impossible.
92 13 42 37 113 10100 40 1002 11 22 21 21 3278695413278695415 26250314066439986238782 581370817372 409476934981 287439719777 7376379831825 616753575719321037808624 222034505841 214063039282 441536506916 4640979418195 431813672576393004301966 405902283416 900951084746 672201172466 518769038906
3 1 4 -1 -1 0 3119 28999960732 -1
In the first test case, $$$k = 1$$$. You can make all the numbers on the blackboard equal to $$$2$$$ with the following operations:
This makes all the numbers equal in $$$3$$$ operations. It can be shown that you cannot make all the numbers equal in less than $$$3$$$ operations.
In the second test case, $$$k = 3$$$. You can make all the numbers on the blackboard equal to $$$7$$$ with the following operation:
In the third test case, $$$k = 10$$$. You can make all the numbers on the blackboard equal to $$$40$$$ with the following operations:
In the fourth and in the fifth test case, you can show that it is impossible to make all the numbers on the blackboard equal.
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