G. Partitionstime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou are given a set of n elements indexed from 1 to n. The weight of i-th element is wi. The weight of some subset of a given set is denoted as . The weight of some partition R of a given set into k subsets is  (recall that a partition of a given set is a set of its subsets such that every element of the given set belongs to exactly one subset in partition).Calculate the sum of weights of all partitions of a given set into exactly k non-empty subsets, and print it modulo 109 + 7. Two partitions are considered different iff there exist two elements x and y such that they belong to the same set in one of the partitions, and to different sets in another partition.InputThe first line contains two integers n and k (1 ≤ k ≤ n ≤ 2·105) — the number of elements and the number of subsets in each partition, respectively.The second line contains n integers wi (1 ≤ wi ≤ 109)— weights of elements of the set.OutputPrint one integer — the sum of weights of all partitions of a given set into k non-empty subsets, taken modulo 109 + 7.ExamplesInput4 22 3 2 3Output160Input5 21 2 3 4 5Output645NotePossible partitions in the first sample:  {{1, 2, 3}, {4}}, W(R) = 3·(w1 + w2 + w3) + 1·w4 = 24;  {{1, 2, 4}, {3}}, W(R) = 26;  {{1, 3, 4}, {2}}, W(R) = 24;  {{1, 2}, {3, 4}}, W(R) = 2·(w1 + w2) + 2·(w3 + w4) = 20;  {{1, 3}, {2, 4}}, W(R) = 20;  {{1, 4}, {2, 3}}, W(R) = 20;  {{1}, {2, 3, 4}}, W(R) = 26; Possible partitions in the second sample:  {{1, 2, 3, 4}, {5}}, W(R) = 45;  {{1, 2, 3, 5}, {4}}, W(R) = 48;  {{1, 2, 4, 5}, {3}}, W(R) = 51;  {{1, 3, 4, 5}, {2}}, W(R) = 54;  {{2, 3, 4, 5}, {1}}, W(R) = 57;  {{1, 2, 3}, {4, 5}}, W(R) = 36;  {{1, 2, 4}, {3, 5}}, W(R) = 37;  {{1, 2, 5}, {3, 4}}, W(R) = 38;  {{1, 3, 4}, {2, 5}}, W(R) = 38;  {{1, 3, 5}, {2, 4}}, W(R) = 39;  {{1, 4, 5}, {2, 3}}, W(R) = 40;  {{2, 3, 4}, {1, 5}}, W(R) = 39;  {{2, 3, 5}, {1, 4}}, W(R) = 40;  {{2, 4, 5}, {1, 3}}, W(R) = 41;  {{3, 4, 5}, {1, 2}}, W(R) = 42. 
Input4 22 3 2 3
Output160
['combinatorics', 'math', 'number theory', '*2700']