302730: CF530C. Diophantine equation

Memory Limit:256 MB Time Limit:2 S
Judge Style:Text Compare Creator:
Submit:0 Solved:0

Description

C. Diophantine equationtime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard output

You 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.

ExamplesInput
3 5 35
Output
2
5 4
10 1
Input
3 35 5
Output
0

Input

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