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Marathon weekend with restrictions

Ackermann Function

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:

prb1111

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 0m3. 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).

Time limit 1 second
Memory limit 128 MiB
Input example #1
1 3
2 4
Output example #1
5
11
Source Stage II All-Ukrainian Olympiad 2010-2011 Berdichev