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2019-03-18 13:00 UTC

Kattis Set 09

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2019-03-25 09:29 UTC
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Problem C
Sums

Given an integer $N$, express it as the sum of at least two consecutive positive integers. For example:

  • $10 = 1 + 2 + 3 + 4$

  • $24 = 7 + 8 + 9$

If there are multiple solutions, output the one with the smallest possible number of summands.

Input

The first line of input contains the number of test cases $T$ ($1 \leq T \leq 2\, 000$). The descriptions of the test cases follow:

Each test case consists of one line containing an integer $N$ ($1 \leq N \leq 10^9$).

Output

For each test case, output a single line containing the equation in the format $N = a + (a+1) + \ldots + b$ as in the example. If there is no solution, output a single word IMPOSSIBLE instead.

Sample Input 1 Sample Output 1
3
8
10
24
IMPOSSIBLE
10 = 1 + 2 + 3 + 4
24 = 7 + 8 + 9