{"problem":{"name":"Max-Min Sums","description":{"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"},"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 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.\nSince the answer can be enormous, print it $\\bmod (10^9+7)$.\n\n## Constraints\n\n*   $1 \\leq N \\leq 10^5$\n*   $1 \\leq K \\leq N$\n*   $|A_i| \\leq 10^9$\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$ $K$\n$A_1$ $...$ $A_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc151_e","tags":[],"sample_group":[["4 2\n1 1 3 4","11\n\nThere 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 $11$."],["6 3\n10 10 10 -10 -10 -10","360\n\nThere are $20$ ways to choose $S$. In $18$ of them, $f(S)=20$, and in $2$ of them, $f(S)=0$."],["3 1\n1 1 1","0"],["10 6\n1000000000 1000000000 1000000000 1000000000 1000000000 0 0 0 0 0","999998537\n\nPrint the sum $\\bmod (10^9+7)$."]],"created_at":"2026-03-03 11:01:14"}}