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 C (GCC 5.4.1) (judge verdict: Wrong Answer)

/*  AUTHOR:AKASH JAIN
*   USERNAME:akash19jain    
*   DATE:27/10/2019 
*/
// #include<algorithm>
// #include <bits/stdc++.h>
// using namespace std;
 
#include<stdio.h>
#include<math.h>
#include<string.h>
#include<stdlib.h>
#include<stdbool.h>
#include<ctype.h>
#define SC1(x)          scanf("%lld",&x)
#define SC2(x,y)        scanf("%lld%lld",&x,&y)
#define SC3(x,y,z)      scanf("%lld%lld%lld",&x,&y,&z)
#define SCS(x)          scanf("\n%s", x)
#define SCA(a,n)        for(long long i=0;i<n;i++)    scanf("%lld",&a[i]);
#define PF1(x)          printf("%lld\n",x)
#define PF2(x,y)        printf("%lld %lld\n",x,y)
#define PF3(x,y,z)      printf("%lld %lld %lld\n",x,y,z)
#define PFA(a,n)        for(long long i=0;i<n;i++)    printf("%lld",a[i]); printf("\n");
#define PFN                printf("\n")
#define REP(i,n)        for(long long i=0;i<(n);++i)
#define FOR(i,a,b)      for(long long i=(a);i<=(b);++i)
#define FORD(i,a,b)     for(long long i=(a);i>=(b);--i)
#define WHILE(n)        while(n--)
#define MEM(a, b)       memset(a, (b), sizeof(a))
#define ITOC(c)         ((char)(((ll)'0')+c))
#define MID(s,e)        (s+(e-s)/2)
#define SZ(a)            strlen(a)
#define MOD             1000000007
#define MAX             10000000005
#define MIN             -10000000005
#define PI              3.1415926535897932384626433832795
#define DEB(x)          printf("The value of \"%s\" is: %d\n",#x,x)
#define CASES           ll t;SC1(t);while(t--)
#define ABS(a)          ((a>0)?a:-(a))
#define SWAP(a,b)        ll z=a;a=b;b=z
#define SWAPC(a,b)        char z=a;a=b;b=z
 
const int INF = 1<<29;
typedef long long ll;
typedef unsigned long long ull;
#define FILEIO(name) \  freopen(name".in", "r", stdin); \   freopen(name".out", "w", stdout);
int cmp(const void * a,const void * b);
long long maxv(long long a,long long b);
long long minv(long long a,long long b);
long long gcd(long long u,long long v);
long long digits(long long n);
bool ispoweroftwo(long long n);
bool isvowel(char x);
ll chartoint(char ch);
ll CEIL(ll x,ll y);
ll FLOOR(ll x,ll y);
int main()
{
        ll n,k;
        SC2(n,k);
        ll arr[n];
        SCA(arr,n);
        ll ans=0;
        REP(i,n)
        {
            ll a=0,b=0;
            FORD(j,i-1,0)
            {
                if(arr[i]>arr[j])
                    b++;
            }
            FOR(j,i+1,n-1)
            {
                if(arr[i]>arr[j])
                    a++;
            }
            ans+=(a*((k*(k+1))/2))+(b*((k*(k-1))/2));
            ans=ans%MOD;
        }
        PF1(ans);

    return 0;
}
 
 
//qsort(arr,n,sizeof(arr[0]),cmp);
int cmp (const void * a, const void * b)
{
    if( *(ll*)a - *(ll*)b < 0 ) return -1;
    if( *(ll*)a - *(ll*)b > 0 ) return 1;
        return 0;
}
long long maxv(long long a,long long b)
{
    if(a>b) return a;
        return b;
}
long long minv(long long a,long long b)
{
    if(a<b) return a;
        return b;
}
long long gcd(long long u,long long v)
{
    if (v == 0) return u; 
       return gcd(v, u%v);
}
long long digits(long long n)    //to calculate no of digits in a number
{
    return floor(log10(n))+1;
}
bool ispoweroftwo(long long x)
{
    return x && (!(x&(x-1)));
}
bool isvowel(char x)
{
    return(x=='a' || x== 'e' ||x=='i' || x== 'o' || x=='u' );
}
ll chartoint(char ch)
{
    if(ch>='A' && ch<='Z') return(ch-'A');
    else if(ch>='0' && ch<='9') return (ch-'0');
    else if(ch>='a' && ch<='z') return (ch-'a');
    else return 0;
}
ll CEIL(ll x,ll y)
{
    if(x%y==0) return(x/y);
    else return(x/y +1);
}
 
ll FLOOR(ll x,ll y)
{
    if(x%y==0) return(x/y);
    else return(x/y -1);
}