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: Runtime Error)

import java.math.BigInteger;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		@SuppressWarnings("resource")
		Scanner scanner = new Scanner(System.in);

		int N = scanner.nextInt();

		int K = scanner.nextInt();

//		long N = scanner.nextLong();
//
//		long ans =0;
//		for(long index=0; index < N; index++) {
//			ans+=index+1;
//		}
//
//		log(ans-N);

		int[] scannerArray = new int[N];

		for (int index = 0; index < N; index++) {
			scannerArray[index] = scanner.nextInt();
		}

		long tmp = countSwapBabbleSort(scannerArray);

		long pair = 0;

		for(int indexI = 0; indexI < N; indexI++) {
			for(int indexJ = 0; indexJ < N; indexJ++) {
				if(scannerArray[indexI] > scannerArray[indexJ]) {
					pair++;
				}
			}
		}

		BigInteger pairOfK = BigInteger.valueOf((long)pair)
				.remainder(BigInteger.valueOf((long)1000000007))
				.multiply((BigInteger.valueOf((long)K))
				.multiply(((BigInteger.valueOf((long)K)).subtract(BigInteger.ONE))
				.divide(BigInteger.valueOf((long)2)))
				.remainder(BigInteger.valueOf((long)1000000007)));
		log(BigInteger.valueOf((long)tmp).multiply(BigInteger.valueOf((long)K))
				.remainder(BigInteger.valueOf((long)1000000007))
				.add(pairOfK)
				.remainder(BigInteger.valueOf((long)1000000007)));

//		log((
//				(BigInteger.valueOf((long)tmp)
//				.multiply(BigInteger.valueOf((long)K)
//						))
//				.add((
//						BigInteger.valueOf((long)tmp)
//						.multiply(
//								BigInteger.valueOf((long)K)
//								.multiply(
//										BigInteger.valueOf((long)K)
//										.subtract(BigInteger.ONE)
//										)
//								.divide(BigInteger.valueOf((long)2)
//										)
//								)
//						)))
//				.remainder(
//						BigInteger.valueOf((long)1000000007)
//						)
//				);
	}


	/**
	 * バブルソートの交換数を算出
	 * ※転倒数
	 * @param array
	 * @return
	 */
	private static long countSwapBabbleSort(int[] array) {
		long ans = 0;
		int[] binary = new int[array.length + 1];

		for (int index = 0; index < array.length; index++) {
			ans = ans + (index - sum(binary, array[index]));
			add(binary, array[index], 1);
		}
		return ans;
	}

    //add value at idx on bit O(logN)
	private static void add(int[] bit,int idx,int value) {
        for(int i=idx;i<bit.length;i=i+(i&-i)) {
        	bit[i] += value;
        }
    }

    //return sum [1,idx] O(logN)
	private static int sum(int[] bit,int idx) {
        int ret = 0;
        for(int i=idx;i>0;i-=(i&-i)) {
        	ret += bit[i];
        }
        return ret;
    }

	private static void log(String str) {
		System.out.println(str);
	}

	private static void log(int str) {
		System.out.println(str);
	}

	private static void log(long str) {
		System.out.println(str);
	}

	private static void log(double str) {
		System.out.println(str);
	}

	private static void log(BigInteger str) {
		System.out.println(str);
	}

}