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