# Problem
# A partial permutation is an ordering of only k objects taken from a collection containing n objects (i.e., k≤n). For example, one partial permutation of three of the first eight positive integers is given by (5,7,2).
# The statistic P(n,k) counts the total number of partial permutations of k objects that can be formed from a collection of n objects. Note that P(n,n) is just the number of permutations of n objects, which we found to be equal to n!=n(n−1)(n−2)⋯(3)(2) in “Enumerating Gene Orders”.
# Given: Positive integers n and k such that 100≥n>0 and 10≥k>0.
# Return: The total number of partial permutations P(n,k), modulo 1,000,000.
# Sample Dataset
# 21 7
# Sample Output
# 51200
# 这道题目中，给定两个正整数 n 和 k（满足 100≥n>0、10≥k>0），定义 P(n,k) 为从 n 个不同的对象中取 k 个对象进行排列的方案数，其中对象排列的顺序有限制（即只能考虑部分的排列方案），计算并输出 P(n,k) 对 1,000,000 取模后的结果。
# 具体来说，P(n,k) 的计算方式为：P(n,k) = n*(n-1)...(n-k+1)。需要注意的是，该计算结果需要对 1,000,000 取模。
def partial_permutations(n, k):
# 初始化P(n,k)为1
P =1
# 计算 P(n,k) 为n*(n-1)* ... *(n-k+1)
for iin range(n, n - k, -1):
P = (P * i) %1000000
return P
print(partial_permutations(21, 7))
