The mean of three integers a, b and c is (a + b + c) / 3. The median of three integers is the one that would be in the middle if they are sorted in non-decreasing order.

Given two integers a and b, return the minimum possible integer c such that the mean and the median of a, b and c are equal.

Input

Each test case is given in a single line that contains two integers a and b (1 ≤ a ≤ b ≤ 109). The last test case is followed by a line containing two zeros.

Output

For each test case output one line containing the minimum possible integer c such that the mean and the median of a, b and c are equal.