C. Kuroni and Impossible Calculationtime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputTo 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.InputThe 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).OutputOutput the single number — \prod_{1\le i<j\le n} |a_i - a_j| \bmod m.ExamplesInput
2 10
8 5
Output
3Input
3 12
1 4 5
Output
0Input
3 7
1 4 9
Output
1NoteIn 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.
2 10
8 5

3
['brute force', 'combinatorics', 'math', 'number theory', '*1600']