Max-Min Sums

AtCoder

IDabc151_e

Time2000ms

Memory256MB

Difficulty—

For a finite set of integers $X$, let $f(X)=\max X - \min X$. Given are $N$ integers $A_1,...,A_N$. 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. Since the answer can be enormous, print it $\bmod (10^9+7)$. ## Constraints * $1 \leq N \leq 10^5$ * $1 \leq K \leq N$ * $|A_i| \leq 10^9$ ## Input Input is given from Standard Input in the following format: $N$ $K$ $A_1$ $...$ $A_N$ [samples]

Samples

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

Input #4

10 6
1000000000 1000000000 1000000000 1000000000 1000000000 0 0 0 0 0

Output #4

999998537

Print the sum $\bmod (10^9+7)$.

API Response (JSON)

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    "name": "Max-Min Sums",
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      "content": "For a finite set of integers $X$, let $f(X)=\\max X - \\min X$. Given are $N$ integers $A_1,...,A_N$. We will choose $K$ of them and let $S$ be the set of the integers chosen. If we distinguish elements",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc151_e"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "For a finite set of integers $X$, let $f(X)=\\max X - \\min X$.\nGiven are $N$ integers $A_1,...,A_N$.\nWe will choose $K$ of them and let $S$ be the set of the integers chosen. If we distinguish elements...",
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      "language": "English"
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}

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