AtCoder Beginner Contest 151
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Problem Statement
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For a finite set of integers $X$, let $f(X)=\max X - \min X$.
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Given are $N$ integers $A_1,...,A_N$.
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We will choose $K$ of them and let $S$ be the set of the integers chosen. If we distinguish elements with different indices even when their values are the same, there are ${}_N C_K$ ways to make this choice. Find the sum of $f(S)$ over all those ways.
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Since the answer can be enormous, print it $\bmod (10^9+7)$.
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Constraints
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$1 \leq N \leq 10^5$$1 \leq K \leq N$$|A_i| \leq 10^9$
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Input
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Input is given from Standard Input in the following format:
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N K
A_1 ... A_N翻译中…
Output
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Print the answer $\bmod (10^9+7)$.
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样例
Input #1
4 2
1 1 3 4
Output #1
11
There are six ways to choose $S$: $\{1,1\},\{1,3\},\{1,4\},\{1,3\},\{1,4\}, \{3,4\}$ (we distinguish the two $1$s). The value of $f(S)$ for these choices are $0,2,3,2,3,1$, respectively, for the total of $11$.
Input #2
6 3
10 10 10 -10 -10 -10
Output #2
360
There are $20$ ways to choose $S$. In $18$ of them, $f(S)=20$, and in $2$ of them, $f(S)=0$.
Input #3
3 1
1 1 1
Output #3
0
Input #4
10 6
1000000000 1000000000 1000000000 1000000000 1000000000 0 0 0 0 0
Output #4
999998537
Print the sum $\bmod (10^9+7)$.
题目信息
题面与样例版权归 AtCoder 及出题人所有；中文翻译由 AI 生成（CI 管线），如有出入请以原文为准。