class Solution {
public:
    double largestSumOfAverages(vector<int>& A, int K) {
//         const int n = A.size();
//         vector<vector<double>> dp(K+1, vector<double>(n+1, 0.0));
//         vector<double> sum(n+1, 0.0);
//         for(int i = 1; i <= n; i++) {
//             sum[i] = sum[i-1] + A[i-1];
//             dp[1][i] = static_cast<double>(sum[i]) / i;
//         }

//         for(int k = 2; k <= K; k++) {
//             for(int i = k; i <= n; i++) {
//                 for(int j = k-1 ; j < i; j++) {
//                     dp[k][i] = max(dp[k][i], dp[k-1][j] + (sum[i] + sum[j])/(i - j));
//                 }
//             }
//         }
//         return dp[K][n];
    const int n = A.size();
    vector<vector<double>> dp(K + 1, vector<double>(n + 1, 0.0));
    vector<double> sums(n + 1, 0.0);
    for (int i = 1; i <= n; ++i) {
      sums[i] = sums[i - 1] + A[i - 1];
      dp[1][i] = static_cast<double>(sums[i]) / i;
    }

    for (int k = 2; k <= K; ++k)
      for (int i = k; i <= n; ++i)
        for (int j = k - 1; j < i; ++j)
          dp[k][i] = max(dp[k][i], dp[k - 1][j] + (sums[i] - sums[j]) / (i - j));

    return dp[K][n];
    }
};