Problem:
Score : 300 points

Problem Statement

We have a sequence of N integers A~=~A_0,~A_1,~...,~A_{N - 1}.

Let B be a sequence of K \times N integers obtained by concatenating K copies of A. For example, if A~=~1,~3,~2 and K~=~2, B~=~1,~3,~2,~1,~3,~2.

Find the inversion number of B, modulo 10^9 + 7.

Here the inversion number of B is defined as the number of ordered pairs of integers (i,~j)~(0 \leq i < j \leq K \times N - 1) such that B_i > B_j.

Constraints

All values in input are integers.

1 \leq N \leq 2000

1 \leq K \leq 10^9

1 \leq A_i \leq 2000

Input

Input is given from Standard Input in the following format:

N K
A_0 A_1 ... A_{N - 1}

Output

Print the inversion number of B, modulo 10^9 + 7.

Sample Input 1

2 2
2 1

Sample Output 1

3

In this case, B~=~2,~1,~2,~1. We have:

B_0 > B_1

B_0 > B_3

B_2 > B_3

Thus, the inversion number of B is 3.

Sample Input 2

3 5
1 1 1

Sample Output 2

0

A may contain multiple occurrences of the same number.

Sample Input 3

10 998244353
10 9 8 7 5 6 3 4 2 1

Sample Output 3

185297239

Be sure to print the output modulo 10^9 + 7.

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        BKleeneInversion solver = new BKleeneInversion();
        solver.solve(1, in, out);
        out.close();
    }

    static class BKleeneInversion {
        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int n = in.readInt();
            long k = in.readLong();
            int[] a = in.readIntArray(n);
            MiscUtils.decreaseByOne(a);

            long sum = 0;
            long diff = n * (n - 1) / 2;
            FenwickTree tree = new FenwickTree(2020);
            for (int i : a) {
                sum += tree.get(i + 1, 2019);
                diff -= tree.get(i, i);
                tree.add(i, 1);
            }

            Modulo.mod = MiscUtils.MOD7;
            Modulo ans = new Modulo(sum).mlt(k);
            Modulo tmp = new Modulo(diff).mlt(k * (k - 1) / 2);
            ans.add(tmp);
            out.printLine(ans);
        }

    }

    static class MiscUtils {
        public static final int MOD7 = (int) (1e9 + 7);

        public static void decreaseByOne(int[]... arrays) {
            for (int[] array : arrays) {
                for (int i = 0; i < array.length; i++) {
                    array[i]--;
                }
            }
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int[] readIntArray(int size) {
            int[] array = new int[size];
            for (int i = 0; i < size; i++) {
                array[i] = readInt();
            }
            return array;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int readInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public long readLong() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void print(Object... objects) {
            for (int i = 0; i < objects.length; i++) {
                if (i != 0) {
                    writer.print(' ');
                }
                writer.print(objects[i]);
            }
        }

        public void printLine(Object... objects) {
            print(objects);
            writer.println();
        }

        public void close() {
            writer.close();
        }

    }

    static class Modulo {
        public static long mod;
        private long value;

        public Modulo(long value) {
            this.value = (value % mod + mod) % mod;
        }

        public static long add(long a, long b) {
            return ((a + b) % mod + mod) % mod;
        }

        public static long mlt(long a, long b) {
            return ((a % mod + mod) * (b % mod + mod)) % mod;
        }

        public Modulo add(long a) {
            setValue(add(value, a));
            return this;
        }

        public Modulo add(Modulo m) {
            return add(m.getValue());
        }

        public Modulo mlt(long a) {
            setValue(mlt(value, a));
            return this;
        }

        public long getValue() {
            return value;
        }

        public void setValue(long value) {
            this.value = value;
        }

        public String toString() {
            return "" + value;
        }

    }

    static class FenwickTree {
        private final long[] value;

        public FenwickTree(int size) {
            value = new long[size];
        }

        public long get(int from, int to) {
            if (from > to) {
                return 0;
            }
            return get(to) - get(from - 1);
        }

        private long get(int to) {
            to = Math.min(to, value.length - 1);
            long result = 0;
            while (to >= 0) {
                result += value[to];
                to = (to & (to + 1)) - 1;
            }
            return result;
        }

        public void add(int at, long value) {
            while (at < this.value.length) {
                this.value[at] += value;
                at = at | (at + 1);
            }
        }

    }
}