# PPER: Partial Permutations

A partial permutation is an ordering of only objects taken from a collection containing objects (i.e., ). For example, one partial permutation of three of the first eight positive integers is given by .

The statistic counts the total number of partial permutations of objects that can be formed from a collection of objects. Note that is just the number of permutations of objects, which we found to be equal to in “Enumerating Gene Orders”.

Given: Positive integers and such that and .

Return: The total number of partial permutations , modulo 1,000,000.

## Sample Dataset

```
21 7
```

## Sample Output

```
51200
```

# R

```
library(magrittr)
f <- "pper.txt"
x <-
readLines(f) %>%
strsplit(split = " ") %>%
unlist() %>%
as.numeric()
n <- x[1]
k <- x[2]
cat((prod(1:n) / prod(1:(n - k))) %% 1E6)
```

```
51200
```