A13173. Kuroni and Impossible Calculation

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 $1\le i < j \le n$ .

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 $a_1, a_2, \dots, a_n$ ( $0 \le a_i \le 10^9$ ).

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

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, $|1 - 4|\cdot|1 - 9|\cdot|4 - 9| = 3 \cdot 8 \cdot 5 = 120 \equiv 1 \bmod 7$ .