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C. Kuroni and Impossible Calculation

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

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

Input

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

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

Examples

Input

2 10 8 5

Output

3

Input

3 12 1 4 5

Output

0

Input

3 7 1 4 9

Output

1

Note

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

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

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