74 - ZOJ Monthly, January 2009 - A
Breadtree is a kind of tree that produces bread. At its first year, a breadtree is only a node with a bread of weight 0 on this node which is also called zeronode. Every year after that, the weight of bread on each node of the tree will increase by 1, and another branch with a zeronode will grow at the end of each node. However, there is a limit of branches on each node. That is, when the number of branches of a node reaches the limit, there won't be any more branches, but the weight of its bread will still increase. What's more, a breadtree remains unchanged when the total weight of bread is larger than 1234567890.
There are two integers N and K on each line. N is a positive integer fit in signed 32-bit integer. K is a non-negative integer fit in signed 32-bit integer. An N equals to 0 signals the end of input, which should not be processed.
Output the total weight of bread on a breadtree with branches limit K in the N-th year in a line for each case.
10000 0 101 1 10 2 1221 128 0 0
9999 5050 221 2147483647
Author: GAO, Yuan
Source: ZOJ Monthly, January 2009