Product of Array Except Self

Given an integer array A of length n (which may contain positive, negative, or zero values), compute an output array B such that for every index i,

$$ B_i = \prod_{\substack{j=0 \\ j \neq i}}^{n-1} A_j $$

This means that every element B[i] is equal to the product of all elements in A except the one at index i. You are required to implement the solution for multiple test cases.

Note: It is guaranteed that the product of elements (except self) will fit into the range of a 64-bit integer.

inputFormat

The input consists of multiple test cases. The first line contains an integer T, representing the number of test cases.

Each of the next T lines describes a test case. Each test case starts with an integer n, the size of the array, followed by n space-separated integers representing the array A.

Example:

2
4 1 2 3 4
3 -1 1 0

outputFormat

For each test case, output a single line containing the resulting array B with n space-separated integers. The output for each test case should be on a new line.

Example:

24 12 8 6
0 0 -1

## sample

2
4 1 2 3 4
3 -1 1 0

24 12 8 6
0 0 -1

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