Spirals

Interview

Time limit1sMemory limit128 MB

Summary

Place the numbers x through y into a square-ish grid spiraling counter-clockwise outward from x at the center, then print the grid with numbers right-aligned to the width of y.

Level: Medium4 of 10
Topics: Matrix, Simulation, Implementation
Solved: No attempts yet

Problem

You are given two positive integers $x$ and $y$ , both less than $100$ . Print the integers from $x$ to $y$ inclusive, laid out in a spiral. You may assume that the end value $y$ is greater than or equal to the start value $x$ .

The spiral begins with the first number $x$ in the centre. The next number is placed immediately below the first number. From there the numbers keep increasing by $1$ , winding outward in a counter-clockwise direction, until the last number $y$ has been placed.

Input

The first line contains the start value $x$ ; the second line contains the end value $y$ . Both are positive integers less than $100$ , and $x \le y$ .

Output

Print the grid of numbers from $x$ to $y$ arranged in the spiral. Within each row the numbers are separated by a single space, and every number is right-aligned to the width of the largest number (that is, $y$ , by its digit count).

Examples2

Example 1

Input

10
27

Expected output

      27 26
16 15 14 25
17 10 13 24
18 11 12 23
19 20 21 22

Example 2
Input
```
7
12
```
Expected output
```
12 11
 7 10
 8  9
```