G. Unusual Calculator
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

At the elective course in electronics, students have developed an unusual calculator. It displays not one number on the screen, but two, and supports three types of commands:

  1. from (m, n) get (m - n, n)
  2. from (m, n) get (m + n, n)
  3. from (m, n) get (n, m)

Determine the sequence of commands to obtain the pair (c, d) from the pair of numbers (a, b).

Input

The first line contains two integers a and b, and the second line contains two integers c and d ($$$-10^5 \le a, b, c, d \le 10^5$$$, $$$a \ne c$$$ or $$$b \ne d$$$).

Output

Output a single line consisting only of digits 1, 2, and 3 without spaces — the command numbers. You do not need to minimize the number of commands, but it should not exceed $$$10^6$$$. During calculations, numbers greater than $$$10^{18}$$$ in absolute value should not be obtained.

If there is no solution, output "IMPOSSIBLE" (without quotes, all uppercase).

Examples
Input
-3 5
3 2
Output
231
Input
3 6
2 3
Output
IMPOSSIBLE