Ackermann Function

Time Limit: 1000 mSec

Memory Limit: 32768 KB

Description

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 of the input will have a two integers, namely m, n, where 0 < m <= 3.
Note that when m<3, n can be any integer less than 1000000, while m=3, the value of n is restricted within 24.
Input is terminated by end of file.

Output

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

Sample Input

1 3
2 4

Sample Output

5
11

Hint

Source

chenyan

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