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combinatorics

math

number theory

*2700

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G. Partitions

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou 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 . 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 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.

Input

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.

Output

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

Examples

Input

4 2

2 3 2 3

Output

160

Input

5 2

1 2 3 4 5

Output

645

Note

Possible partitions in the first sample:

- {{1, 2, 3}, {4}},
*W*(*R*) = 3·(*w*_{1}+*w*_{2}+*w*_{3}) + 1·*w*_{4}= 24; - {{1, 2, 4}, {3}},
*W*(*R*) = 26; - {{1, 3, 4}, {2}},
*W*(*R*) = 24; - {{1, 2}, {3, 4}},
*W*(*R*) = 2·(*w*_{1}+*w*_{2}) + 2·(*w*_{3}+*w*_{4}) = 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.

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

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