As is known, Ackermann function plays an important role in the sphere of theoretical computer science. However, in the other hand, the dramatic fast increasing pace of the function caused the value of Ackermann function hard to calcuate.

Ackermann function can be defined recursively as follows:

Given m and n, your task is to compute the value of A(m, n).

Input

Each line has two integers m and n, where 0 ≤ m ≤ 3. Note that when m < 3, n can be any integer less than 106, while m = 3, the value of n is restricted within 24.

Output

For each value of m and n print the value of A(m, n).