Partitions

2000ms

262144K

Description:

You are given a set of n elements indexed from 1 to n. The weight of i-th element is w_i. The weight of some subset of a given set is denoted as $\text{[math]}$ . The weight of some partition R of a given set into k subsets is $\text{[math]}$ (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.

Input:

The 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 w_i (1 ≤ w_i ≤ 10⁹)— weights of elements of the set.

Output:

Print one integer — the sum of weights of all partitions of a given set into k non-empty subsets, taken modulo 10⁹ + 7.

Sample Input:

4 2
2 3 2 3

Sample Output:

Sample Input:

5 2
1 2 3 4 5

Sample Output:

Note:

Possible 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.

Informação

Provedor Codeforces

Código CF961G