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VK Cup 2015 - Wild Card Round 1:

- Picat 0.9

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C. Diophantine equation

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou are given an equation *A* * *X* + *B* * *Y* = *C*, *A*, *B*, *C* are positive integer coefficients, *X* and *Y* are variables which can have positive integer values only. Output the number of solutions of this equation and the solutions themselves.

Input

The only line of input contains integers *A*, *B* and *C* (1 ≤ *A*, *B*, *C* ≤ 1000), separated with spaces.

Output

In the first line of the output print the number of the solutions *N*. In the next *N* lines print the solutions, formatted as "*XY*", sorted in ascending order of *X*, one solution per line.

Examples

Input

3 5 35

Output

2

5 4

10 1

Input

3 35 5

Output

0

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