题目描述

Bobo has a point A in the n dimension real space $\mathbb{R}^n$ , whose coodinate is $(a_1 / m, a_2 / m, \dots, a_n / m)$ where $a_i$ and m are both integers. He wants to find another point $P = (p_1, p_2, \dots, p_n)$ meeting the following requirements.

• $p_1, p_2, \dots, p_n \in \mathbb{R}$ . That is, they are real numbers.
• $p_1, p_2, \dots, p_n \geq 0$
• $p_1 + p_2 + \dots + p_n = 1$
• The (squared) Euclidean distance between P and A, which is $\|A - P\|_2^2 = \sum_{i = 1}^n (a_i / m - p_i)^2$, is minimized.

It can be proved the minimum is always a rational number. Print the squared distance in fraction. Note to print an integer n as n instead of n/1.

输入格式

The input consists of several test cases and is terminated by end-of-file.

The first line of each test case contains two integers n and m. The second line contains n integers $a_1, a_2, \dots, a_n$.

• $1 \leq n \leq 10^4$
• $1 \leq m \leq 10^3$
• $-m \leq a_i \leq m$
• The sum of n does not exceed $5 \times 10^5$.

输出格式

For each test case, print a fraction which denotes the result.

样例

样例输入 1

1 1
0
2 3
1 2
3 10
1 -2 3

样例输出 1

1
0
16/75