Product of differences

Easy

Execution time limit is 1 second

Runtime memory usage limit is 128 megabytes

Array of integers $a_{1}, a_{2}, ..., a_{n}$ is given. Find the product

1 \leq i < j \leq n \prod ∣ a_{i} - a_{j} ∣

If you are not familiar with short notation, this product equals to

∣ a_{1} - a_{2} ∣ * ∣ a_{1} - a_{3} ∣ * ... * ∣ a_{1} - a_{n} ∣ * ∣ a_{2} - a_{3} ∣ * ∣ a_{2} - a_{4} ∣ * ... * ∣ a_{2} - a_{n} ∣ * ... * ∣ a_{n - 1} - a_{n} ∣

In other words, this is the product of $∣ a_{i} - a_{j} ∣$ for all $1 \leq i < j \leq n$ .

As the result will be very big, find it modulo $m$ .

Input

First line contains two integers $n (n \leq 1 0^{5})$ and $m (m \leq 1000)$ . Next line contains $n$ integers $a_{1}, a_{2}, ..., a_{n} (0 \leq a_{i} \leq 1 0^{9})$ .

Output

Print the value of the product modulo $m$ .

Examples

Input #1

Answer #1

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