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.
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 $N$ ($1 \leq N \leq 10^9$).
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 |