Let S = x_{1}, …, x_{n}
be a sequence of integer numbers
such that x_{1} < … < x_{n}.
For every integer number a and every index 1 ≤ i ≤ 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}, …, a_{m}.
Assume 1 ≤ n ≤ 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.

Public test cases

**Input**

5 -7 -2 0 4 8 1 0 5 0 1 2 3 4 3 0 -1 1

**Output**

Sequence #1 fixed point for 0: 4 Sequence #2 no fixed point for 0 no fixed point for -1 fixed point for 1: 1

Information

- Author
- Salvador Roura
- Language
- English
- Official solutions
- C++ Python
- User solutions
- C++ Python