# Partitions

## 题目描述

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 ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF961G/fbf0c843290b6183affbaf7ada0d6cecd6d2fbbd.png). The weight of some partition $R$ of a given set into $k$ subsets is ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF961G/0aeb77393cfc4b9aa3d9c64303202277f9c1f051.png) (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 $10^{9}+7$ . 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.

## 输入输出格式

### 输入格式

The first line contains two integers $n$ and $k$ ( $1<=k<=n<=2·10^{5}$ ) — the number of elements and the number of subsets in each partition, respectively. The second line contains $n$ integers $w_{i}$ ( $1<=w_{i}<=10^{9}$ )— weights of elements of the set.

### 输出格式

Print one integer — the sum of weights of all partitions of a given set into $k$ non-empty subsets, taken modulo $10^{9}+7$ .

## 输入输出样例

### 输入样例 #1

4 2
2 3 2 3


### 输出样例 #1

160


### 输入样例 #2

5 2
1 2 3 4 5


### 输出样例 #2

645


## 说明

Possible partitions in the first sample: 1. $\{\{1,2,3\},\{4\}\}$ , $W(R)=3\cdot(w_{1}+w_{2}+w_{3})+1\cdot w_{4}=24$ ; 2. $\{\{1,2,4\},\{3\}\}$ , $W(R)=26$ ; 3. $\{\{1,3,4\},\{2\}\}$ , $W(R)=24$ ; 4. $\{\{1,2\},\{3,4\}\}$ , $W(R)=2\cdot(w_{1}+w_{2})+2\cdot(w_{3}+w_{4})=20$ ; 5. $\{\{1,3\},\{2,4\}\}$ , $W(R)=20$ ; 6. $\{\{1,4\},\{2,3\}\}$ , $W(R)=20$ ; 7. $\{\{1\},\{2,3,4\}\}$ , $W(R)=26$ ; Possible partitions in the second sample: 1. $\{\{1,2,3,4\},\{5\}\}$ , $W(R)=45$ ; 2. $\{\{1,2,3,5\},\{4\}\}$ , $W(R)=48$ ; 3. $\{\{1,2,4,5\},\{3\}\}$ , $W(R)=51$ ; 4. $\{\{1,3,4,5\},\{2\}\}$ , $W(R)=54$ ; 5. $\{\{2,3,4,5\},\{1\}\}$ , $W(R)=57$ ; 6. $\{\{1,2,3\},\{4,5\}\}$ , $W(R)=36$ ; 7. $\{\{1,2,4\},\{3,5\}\}$ , $W(R)=37$ ; 8. $\{\{1,2,5\},\{3,4\}\}$ , $W(R)=38$ ; 9. $\{\{1,3,4\},\{2,5\}\}$ , $W(R)=38$ ; 10. $\{\{1,3,5\},\{2,4\}\}$ , $W(R)=39$ ; 11. $\{\{1,4,5\},\{2,3\}\}$ , $W(R)=40$ ; 12. $\{\{2,3,4\},\{1,5\}\}$ , $W(R)=39$ ; 13. $\{\{2,3,5\},\{1,4\}\}$ , $W(R)=40$ ; 14. $\{\{2,4,5\},\{1,3\}\}$ , $W(R)=41$ ; 15. $\{\{3,4,5\},\{1,2\}\}$ , $W(R)=42$ .