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#F2271. Levko and Sets

    ID: 2277 传统题 2000ms 256MiB 尝试: 0 已通过: 0 难度: 9 上传者: 标签>数论数学挑战难度共享题库Codeforces英文题面题目来源题面语言

Levko and Sets

题目描述

D. Levko and Sets
time limit per test
3 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Levko loves all sorts of sets very much.

Levko has two arrays of integers a1,a2,... ,an and b1,b2,... ,bm and a prime number p. Today he generates n sets. Let's describe the generation process for the i-th set:

  1. First it has a single number 1.
  2. Let's take any element c from this set. For all j (1≤j≤m) if number (c·aibj)modp doesn't occur in the set, then add it to the set.
  3. Repeat step 2 as long as we can add at least one element to our set.

Levko wonders, how many numbers belong to at least one set. That is, he wants to know what size is the union of n generated sets.

Input

The first line contains three integers n, m and p (1≤n≤104, 1≤m≤105, 2≤p≤109), p is prime.

The second line contains space-separated integers a1,a2,... ,an (1≤ai<p). The third line contains space-separated integers b1,b2,... ,bm (1≤bi≤109).

Output

The single number − the size of the union of the sets.

Examples
Input
1 1 7
2
5
Output
3
Input
1 2 7
2
2 4
Output
3
Input
2 1 7
1 6
2
Output
1
Input
2 1 7
1 6
5
Output
2

题目来源：fps-www.educg.net-codeforce-1-2833.xml.zip；FPS 共享题包，题包内第 1883 题。保留原作者与原赛事署名。