class Solution {
public:
    
    int InsertSort(vector<int>& a, int l, int r){
        for(int i = l + 1; i <= r; i++){
            auto x = a[i];
            auto j = i;
            while(j > l && x < a[j-1]){
                a[j] = a[j-1];
                j--;
            }
            a[j] = x;
        }
        return  l + (r - l) / 2;
    }

    int Partiton(vector<int>& a, int l, int r, int m){
        int x = a[m];
        int i = l;
        int j = r;

        swap(a[m], a[l]);
        while(i < j){
            while(i < j && a[j] >= x) j--;
            a[i] = a[j];
            while(i < j && a[i] <= x) i++;
            a[j] = a[i];
        }
        a[i] = x;
        return i;
    }




    int FindMid(vector<int>& a, int l, int r){
        if(r - l + 1 < 5) return InsertSort(a, l, r);
        int p = l - 1;

        for(int i = l; i < r - 5; i += 5){
            int mid = InsertSort(a, i, i+4);

            swap(a[++p], a[mid]);
        }
        return FindMid(a, l, p);
    }

    int BFPRT(vector<int>& a, int l, int r, int k){
        if(l == r) return a[l];

        int m = FindMid(a, l, r);
        int p = Partiton(a, l, r, m);
        int n = p - l + 1;
        if(n == k) return a[p];
        if(n > k) return BFPRT(a, l, p, k);
        return BFPRT(a, p+1, r, k - n);
    }
    
    int findKthLargest(vector<int>& nums, int k) {
        return BFPRT(nums, 0, nums.size()-1, nums.size() - k + 1);
    }
};