The Lost Fraction

Memory limit: 32 MB

Byteasar invented a really cool fraction with denominator not greater than but unfortunately after some time he forgot what fraction it was. He is almost sure that the fraction belongs to the interval . Help him find his fraction.

Input

The only line of the input contains two integers and (, ) separated with a single space.

Output

The first line of the output should contain one integer - the number of fractions with denominators not grater than that belong to the given interval. Each of the following lines should contain two positive integers separated with a single space, denoting the numerator and the denominator of a fraction. Fractions specified in the output should be unique and should all be written in the simplified form. The fractions may be written in any order.

Example

For the input data:

5 43

the correct result is:

1
7 4

Task author: Jakub Pawlewicz.