Algorithm title: UVA 10943

Problem a:how do you add?

The Larry is very bad at Math-he usually uses a calculator, which worked the very throughout. Unforunately, he's now struck in a deserted island with his good buddy Ryan after a snowboarding accident. They ' re now trying to spend some time figuring out some good problems, and Ryan would eat Larry if he cannot answer Fate is up to you!

It ' s a very simple problem-given a number n, how many ways can K numbers less than n add up to n?

For example, for N = there and K = 2, are ways:

0+20

1+19

2+18

3+17

4+16

5+15

...

18+2

19+1

20+0

Input

Each line would contain a pair of numbers n and K. N and K would both be the integer from 1 to, inclusive. The input would terminate on 2 0 ' s.

Output

Since Larry is only interested in the last few digits of the answer, for each pair of numbers N and K, print a single numb ER mod 1,000,000 on a single line.

Sample Input

20 2

20 2

0 0

Sample Output

21st

21st