Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

C. Primitive Primes

time limit per test

1.5 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputIt is Professor R's last class of his teaching career. Every time Professor R taught a class, he gave a special problem for the students to solve. You being his favourite student, put your heart into solving it one last time.

You are given two polynomials $$$f(x) = a_0 + a_1x + \dots + a_{n-1}x^{n-1}$$$ and $$$g(x) = b_0 + b_1x + \dots + b_{m-1}x^{m-1}$$$, with positive integral coefficients. It is guaranteed that the cumulative GCD of the coefficients is equal to $$$1$$$ for both the given polynomials. In other words, $$$gcd(a_0, a_1, \dots, a_{n-1}) = gcd(b_0, b_1, \dots, b_{m-1}) = 1$$$. Let $$$h(x) = f(x)\cdot g(x)$$$. Suppose that $$$h(x) = c_0 + c_1x + \dots + c_{n+m-2}x^{n+m-2}$$$.

You are also given a prime number $$$p$$$. Professor R challenges you to find any $$$t$$$ such that $$$c_t$$$ isn't divisible by $$$p$$$. He guarantees you that under these conditions such $$$t$$$ always exists. If there are several such $$$t$$$, output any of them.

As the input is quite large, please use fast input reading methods.

Input

The first line of the input contains three integers, $$$n$$$, $$$m$$$ and $$$p$$$ ($$$1 \leq n, m \leq 10^6, 2 \leq p \leq 10^9$$$), — $$$n$$$ and $$$m$$$ are the number of terms in $$$f(x)$$$ and $$$g(x)$$$ respectively (one more than the degrees of the respective polynomials) and $$$p$$$ is the given prime number.

It is guaranteed that $$$p$$$ is prime.

The second line contains $$$n$$$ integers $$$a_0, a_1, \dots, a_{n-1}$$$ ($$$1 \leq a_{i} \leq 10^{9}$$$) — $$$a_i$$$ is the coefficient of $$$x^{i}$$$ in $$$f(x)$$$.

The third line contains $$$m$$$ integers $$$b_0, b_1, \dots, b_{m-1}$$$ ($$$1 \leq b_{i} \leq 10^{9}$$$) — $$$b_i$$$ is the coefficient of $$$x^{i}$$$ in $$$g(x)$$$.

Output

Print a single integer $$$t$$$ ($$$0\le t \le n+m-2$$$) — the appropriate power of $$$x$$$ in $$$h(x)$$$ whose coefficient isn't divisible by the given prime $$$p$$$. If there are multiple powers of $$$x$$$ that satisfy the condition, print any.

Examples

Input

3 2 2 1 1 2 2 1

Output

1

Input

2 2 999999937 2 1 3 1

Output

2

Note

In the first test case, $$$f(x)$$$ is $$$2x^2 + x + 1$$$ and $$$g(x)$$$ is $$$x + 2$$$, their product $$$h(x)$$$ being $$$2x^3 + 5x^2 + 3x + 2$$$, so the answer can be 1 or 2 as both 3 and 5 aren't divisible by 2.

In the second test case, $$$f(x)$$$ is $$$x + 2$$$ and $$$g(x)$$$ is $$$x + 3$$$, their product $$$h(x)$$$ being $$$x^2 + 5x + 6$$$, so the answer can be any of the powers as no coefficient is divisible by the given prime.

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Jun/01/2020 09:36:26 (i2).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|