Think Small

Jeongmin has grown up, and his parents now make him work through a well known workbook series called Think Small. The unit he has to study this time is multiplication of polynomials. Jeongmin wants to play games instead, so he offers to share his points if you write the program that multiplies the polynomial $f(x)$ by the polynomial $g(x)$ for him.

The first line contains the degree $N$ of the polynomial $f(x)$ and the degree $M$ of the polynomial $g(x)$, separated by a space. ($1 \le N \le 1{,}000{,}000$, $1 \le M \le 1{,}000{,}000$)

The second line contains $N + 1$ natural numbers $a_0, a_1, \dots, a_N$, the coefficients of $f(x)$, so that $f(x) = a_0 + a_1 x + a_2 x^2 + \dots + a_N x^N$. ($1 \le a_i \le 1{,}000{,}000$)

The third line contains $M + 1$ natural numbers $b_0, b_1, \dots, b_M$, the coefficients of $g(x)$, so that $g(x) = b_0 + b_1 x + b_2 x^2 + \dots + b_M x^M$. ($1 \le b_i \le 1{,}000{,}000$)

Let $f(x) \times g(x) = c_0 + c_1 x + c_2 x^2 + \dots + c_L x^L$.

Print the xor of every coefficient, $c_0 \oplus c_1 \oplus \dots \oplus c_L$, on the first line. In C or C++ you compute c[0] ^ c[1] ^ ... ^ c[L].

The xor is asked for because printing every $c_i$ would be far too much output. It does not change how the problem is solved.

If $f(x) = 1 + 2x$ and $g(x) = 3 + 2x$, then $f(x) \times g(x) = 3 + 8x + 4x^2$.