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.

Examples

Input

3 5 35


Output

2
5 4
10 1


Input

3 35 5


Output

0

Source: codeforces | Difficulty: MEDIUM


Solutions: