Kuroni and Impossible Calculation

题意翻译

- 给定 $n$ 个整数 $a_{1,...,n}$ 和一个整数 $m$。 - 你需要求出 $\prod\limits_{1\le i<j\le n} |a_i-a_j| \bmod m$ 的值。 - $2\le n\le 2\times 10^5$，$1 \le m \le 1000$，$0 \le a_i \le 10^9$。

题目描述

To become the king of Codeforces, Kuroni has to solve the following problem. He is given $ n $ numbers $ a_1, a_2, \dots, a_n $ . Help Kuroni to calculate $ \prod_{1\le i<j\le n} |a_i - a_j| $ . As result can be very big, output it modulo $ m $ . If you are not familiar with short notation, $ \prod_{1\le i<j\le n} |a_i - a_j| $ is equal to $ |a_1 - a_2|\cdot|a_1 - a_3|\cdot $ $ \dots $ $ \cdot|a_1 - a_n|\cdot|a_2 - a_3|\cdot|a_2 - a_4|\cdot $ $ \dots $ $ \cdot|a_2 - a_n| \cdot $ $ \dots $ $ \cdot |a_{n-1} - a_n| $ . In other words, this is the product of $ |a_i - a_j| $ for all $ 1\le i < j \le n $ .

输入输出格式

输入格式

The first line contains two integers $ n $ , $ m $ ( $ 2\le n \le 2\cdot 10^5 $ , $ 1\le m \le 1000 $ ) — number of numbers and modulo. The second line contains $ n $ integers $ a_1, a_2, \dots, a_n $ ( $ 0 \le a_i \le 10^9 $ ).

输出格式

Output the single number — $ \prod_{1\le i<j\le n} |a_i - a_j| \bmod m $ .

输入输出样例

输入样例 #1

2 10
8 5

输出样例 #1

3

输入样例 #2

3 12
1 4 5

输出样例 #2

0

输入样例 #3

3 7
1 4 9

输出样例 #3

1

说明

In the first sample, $ |8 - 5| = 3 \equiv 3 \bmod 10 $ . In the second sample, $ |1 - 4|\cdot|1 - 5|\cdot|4 - 5| = 3\cdot 4 \cdot 1 = 12 \equiv 0 \bmod 12 $ . In the third sample, $ |1 - 4|\cdot|1 - 9|\cdot|4 - 9| = 3 \cdot 8 \cdot 5 = 120 \equiv 1 \bmod 7 $ .