Polynomial Multiplication Under Modulo

You are given two polynomials \( F(x) \) and \( G(x) \). Your task is to compute the product \( F(x) \times G(x) \) modulo a given integer \( p \). Specifically, if the product is \( H(x)=F(x)\times G(x)=\sum_{i=0}^{n+m} h_i x^i \), then each coefficient \( h_i \) should be computed modulo \( p \).

Note: The modulus \( p \) is arbitrary and is not guaranteed to be of the form \( p = a \cdot 2^k + 1 \). Therefore, algorithms that depend on that structure (such as FFT based on that property) may not be applicable.

Input format: See the input description below.

inputFormat

The input contains three lines:

1. The first line contains three integers \( n \), \( m \), and \( p \), where \( n \) and \( m \) represent the degrees of the two polynomials \( F(x) \) and \( G(x) \) respectively, and \( p \) is the modulus.
2. The second line contains \( n+1 \) integers which are the coefficients of \( F(x) \) in increasing order (i.e., from the constant term up to the \( x^n \) term).
3. The third line contains \( m+1 \) integers which are the coefficients of \( G(x) \) in increasing order.

outputFormat

Output a single line containing \( n+m+1 \) integers: the coefficients of the resulting polynomial \( H(x) = F(x) \times G(x) \) modulo \( p \), in increasing order of powers of \( x \).

sample

1 1 7
1 2
3 4

3 3 1