It is well known that Mark likes creating mathematical tasks very much. Recently he has invented the following one: for given find all positive integers and , that A \le B and
One integer (1 \le S \le 10^{12}).
First line at output should contain one integer – number of pairs that have been found. Each of following lines should contain integers, first not greater than second – corresponding pair. Pairs should be printed sorted ascending by first number.
Example 1