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Problems

Ackermann Function

Ackermann Function

Time limit 1 second
Memory limit 128 MiB

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 data

Each line has two integers m and n, where 0m3. Note that when m < 3, n can be any integer less than 10^6, while m = 3, the value of n is restricted within 24.

Output data

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

Examples

Input example #1
1 3
2 4
Output example #1
5
11
Source Stage II All-Ukrainian Olympiad 2010-2011 Berdichev