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Count Pairs

4000ms 262144K

Description:

You are given a prime number $$$p$$$, $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$, and an integer $$$k$$$.

Find the number of pairs of indexes $$$(i, j)$$$ ($$$1 \le i < j \le n$$$) for which $$$(a_i + a_j)(a_i^2 + a_j^2) \equiv k \bmod p$$$.

Input:

The first line contains integers $$$n, p, k$$$ ($$$2 \le n \le 3 \cdot 10^5$$$, $$$2 \le p \le 10^9$$$, $$$0 \le k \le p-1$$$). $$$p$$$ is guaranteed to be prime.

The second line contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$0 \le a_i \le p-1$$$). It is guaranteed that all elements are different.

Output:

Output a single integer — answer to the problem.

Sample Input:

 3 3 0 0 1 2 

Sample Output:

 1

Sample Input:

 6 7 2 1 2 3 4 5 6 

Sample Output:

 3

Note:

In the first example:

$$$(0+1)(0^2 + 1^2) = 1 \equiv 1 \bmod 3$$$.

$$$(0+2)(0^2 + 2^2) = 8 \equiv 2 \bmod 3$$$.

$$$(1+2)(1^2 + 2^2) = 15 \equiv 0 \bmod 3$$$.

So only $$$1$$$ pair satisfies the condition.

In the second example, there are $$$3$$$ such pairs: $$$(1, 5)$$$, $$$(2, 3)$$$, $$$(4, 6)$$$.

Info

CodeForces

Provider CodeForces

Origin Codeforces Round #572 (Div. 1)

Code CF1188B

Tags

mathmatricesnumber theorytwo pointers

Submitted 80

Passed 25

AC Rate 31.25%

Date 07/21/2019 13:44:53

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