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1-------------
#define MOD 1000000007
class Solution {
public:
    int kInversePairs(int n, int k) {
        vector<vector<int>>dp(n+1,vector<int>(k+1,0));
        dp[0][0]=1;
        vector<int>prev(k+1,0);
        prev[0]=1;
       
        for(int i=1;i<=n;i++){
             vector<int>cur(k+1);
            for(int j=0;j<=k;j++){
                for(int p=0;p<i;p++){
                    if(j-p>=0) cur[j]+=prev[j-p]%MOD;
                }
            }
            prev=cur;
        }
        return prev[k]; //prev =cur 
    }
};
2------------------
#define MOD 1000000007
class Solution {
public:
    int kInversePairs(int n, int k) {
        vector<vector<int>>dp(n+1,vector<int>(k+1,0));
        dp[0][0]=1;
        vector<int>prev(k+1,0);
        prev[0]=1;
       
        for(int i=1;i<=n;i++){
            vector<int>cur(k+1);
            int sum=0;
            for(int j=0;j<=k;j++){
                if(j>=i) sum-=prev[j-i];
                sum+=prev[j]%MOD;
                cur[j]=sum;
            }
            prev=cur;
        }
        return prev[k]; //prev =cur 
    }
};
3--------------------------------------
#define MOD 1000000007
class Solution {
public:
    int kInversePairs(int n, int k) {
        vector<vector<int>>dp(n+1,vector<int>(k+1,0));
        dp[0][0]=1;
        vector<int>prev(k+1,0);
        prev[0]=1;
       
        for(int i=1;i<=n;i++){
            vector<int>cur(k+1);
            int sum=0;
            for(int j=0;j<=k;j++){
                if(j>=i) sum=(sum-prev[j-i]+MOD)%MOD;
                sum=(sum+prev[j])%MOD;
                cur[j]=sum;
            }
            prev=cur;
        }
        return prev[k]; //prev =cur 
    }
};