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Problems

Fun function - 2

Fun function - 2

Time limit 1 second
Memory limit 128 MiB

Find the value of the function

f(x, y) = \begin{cases} 1, x \le 0~or~y \le 0 \\ f(x - 1, y) + f(x, y - 1) + 1, x \le y \\ f(x, y / 2) + 2, x > y \end{cases}

Input data

Two integers x, y~(0 \le x, y \le 25).

Output data

Print the value of the function f(x, y).

Examples

Input example #1
2 3
Output example #1
17
Author Mykhailo Medvediev