Fixed points P34682

Let $S = x_1, \dots, x_n$ be a sequence of integer numbers such that $x_1 < \dots < x_n$. For every integer number $a$ and every index $1 \le i \le n$, define $f_a(i) = x_i + a$. Write a program that, given $S$ and $a$, tells whether there is some $i$ such that $f_a(i) = i$.

Input

Input consists of several cases. Every case begins with $n$, followed by $S$, followed by a number $m$, followed by $m$ different integer numbers $a_1, \dots, a_m$. Assume $1 \le n \le 10^6$.

Output

For every case, print its number starting at 1. Afterwards, for every $a_j$ print the position of its fixed point. If no fixed point exists, state so. If there is more than one fixed point, print the smallest one. Print a blank line after the output for every case.