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 ( \left[ \frac{a}{n^2},\frac{a+1}{n^2} \right] ). Help him find his fraction.</p>

입력 형식

The only line of the input contains two integers n and a (1 ≤ n < 2³², 1 ≤ a < 2⁶⁴ - 1) separated with a single space.</p>

출력 형식

The first line of the output should contain one integer m - the number of fractions with denominators not grater than n that belong to the given interval. Each of the following m 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.</p>

예제 입력

5 43

예제 출력

1
7 4