Fixed points

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.

Problem information

Author: Salvador Roura

Generation: 2026-01-25T10:22:29.729Z