[CERC2014] Sums

题意翻译

## 题目大意 一共有 $T$ 组数据,每组数据给定一个数 $N$,请将 $N$ 分解为几个连续正整数的和,如果有多种情况,请输出最小数最大的情况。 ## 输入格式: 第一行,一个整数 $T$,表示数据组数。 第 $2$ 行至第 $T+1$ 行,每行一个整数 $N$,表示要拆分的数字。 ## 输出格式 $T$ 行,每行一个式子,表示拆分结果。 如果无解,请输出 `IMPOSSIBLE`。

题目描述

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.

输入输出格式

输入格式


The first line of input contains the number of test cases $T$. The descriptions of the test cases follow: Each test case consists of one line containing an integer $N(1 \le N \le 10^9)$.

输出格式


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

输入输出样例

输入样例 #1

3
8
10
24

输出样例 #1

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