Problem:
Score : 700 points

Problem Statement

There are N panels arranged in a row in Takahashi's house, numbered 1 through N. The i-th panel has a number A_i written on it. Takahashi is playing by throwing balls at these panels.

Takahashi threw a ball K times. Let the panel hit by a boll in the i-th throw be panel p_i. He set the score for the i-th throw as i \times A_{p_i}.

He was about to calculate the total score for his throws, when he realized that he forgot the panels hit by balls, p_1,p_2,...,p_K. The only fact he remembers is that for every i (1 ≦ i ≦ K-1), 1 ≦ p_{i+1}-p_i ≦ M holds. Based on this fact, find the maximum possible total score for his throws.

Constraints

1 ≦ M ≦ N ≦ 100,000

1 ≦ K ≦ min(300,N)

1 ≦ A_i ≦ 10^{9}

Partial Scores

In the test set worth 100 points, M = N.

In the test set worth another 200 points, N ≦ 300 and K ≦ 30.

In the test set worth another 300 points, K ≦ 30.

Input

The input is given from Standard Input in the following format:

N M K
A_1 A_2 … A_N

Output

Print the maximum possible total score for Takahashi's throws.

Sample Input 1

5 2 3
10 2 8 10 2

Sample Output 1

56

The total score is maximized when panels 1,3 and 4 are hit, in this order.

Sample Input 2

5 5 2
5 2 10 5 9

Sample Output 2

28

This case satisfies the additional constraint M = N for a partial score.

Sample Input 3

10 3 5
3 7 2 6 9 4 8 5 1 1000000000

Sample Output 3

5000000078

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)


import java.util.Arrays;

class SegmentTreeRMQL {
  public int M, H, N;
  public long[] st;

  public SegmentTreeRMQL(int n) {
    N = n;
    M = Integer.highestOneBit(Math.max(N - 1, 1)) << 2;
    H = M >>> 1;
    st = new long[M];
    Arrays.fill(st, 0, M, Long.MAX_VALUE);
  }

  public SegmentTreeRMQL(long[] a) {
    N = a.length;
    M = Integer.highestOneBit(Math.max(N - 1, 1)) << 2;
    H = M >>> 1;
    st = new long[M];
    for (int i = 0; i < N; i++) {
      st[H + i] = a[i];
    }
    Arrays.fill(st, H + N, M, Long.MAX_VALUE);
    for (int i = H - 1; i >= 1; i--)
      propagate(i);
  }

  public void update(int pos, long x) {
    st[H + pos] = x;
    for (int i = (H + pos) >>> 1; i >= 1; i >>>= 1)
      propagate(i);
  }

  private void propagate(int i) {
    st[i] = Math.min(st[2 * i], st[2 * i + 1]);
  }

  public long minx(int l, int r) {
    long min = Long.MAX_VALUE;
    if (l >= r)
      return min;
    while (l != 0) {
      int f = l & -l;
      if (l + f > r)
        break;
      long v = st[(H + l) / f];
      if (v < min)
        min = v;
      l += f;
    }

    while (l < r) {
      int f = r & -r;
      long v = st[(H + r) / f - 1];
      if (v < min)
        min = v;
      r -= f;
    }
    return min;
  }

  public long min(int l, int r) {
    return l >= r ? 0 : min(l, r, 0, H, 1);
  }

  private long min(int l, int r, int cl, int cr, int cur) {
    if (l <= cl && cr <= r) {
      return st[cur];
    } else {
      int mid = cl + cr >>> 1;
      long ret = Long.MAX_VALUE;
      if (cl < r && l < mid) {
        ret = Math.min(ret, min(l, r, cl, mid, 2 * cur));
      }
      if (mid < r && l < cr) {
        ret = Math.min(ret, min(l, r, mid, cr, 2 * cur + 1));
      }
      return ret;
    }
  }

  public int firstle(int l, long v) {
    int cur = H + l;
    while (true) {
      if (st[cur] <= v) {
        if (cur < H) {
          cur = 2 * cur;
        } else {
          return cur - H;
        }
      } else {
        cur++;
        if ((cur & cur - 1) == 0)
          return -1;
        if ((cur & 1) == 0)
          cur >>>= 1;
      }
    }
  }

  public int lastle(int l, long v) {
    int cur = H + l;
    while (true) {
      if (st[cur] <= v) {
        if (cur < H) {
          cur = 2 * cur + 1;
        } else {
          return cur - H;
        }
      } else {
        if ((cur & cur - 1) == 0)
          return -1;
        cur--;
        if ((cur & 1) == 1)
          cur >>>= 1;
      }
    }
  }
}



public class Main {
  private static void solve() {
    int n = ni();
    int m = ni();
    int k = ni();
    int[] a = na(n);
    SegmentTreeRMQL[] dp = new SegmentTreeRMQL[k + 1];
    for (int i = 0; i <= k; i++) {
      dp[i] = new SegmentTreeRMQL(n + 1);
    }
    dp[0].update(0, 0);

    for (int i = 0; i < k; i++) {
      for (int j = 1; j <= n; j++) {
        long v = dp[i].min(Math.max(0, j - m), j);
        dp[i + 1].update(j, v - (long) (i + 1) * a[j - 1]);
      }
    }
    long ret = 0;
    for (int i = 0; i <= n; i++) {
      ret = Math.max(ret, -dp[k].min(0, n + 1));
    }
    System.out.println(ret);
  }

  public static void main(String[] args) {
    new Thread(null, new Runnable() {
      @Override
      public void run() {
        long start = System.currentTimeMillis();
        String debug = args.length > 0 ? args[0] : null;
        if (debug != null) {
          try {
            is = java.nio.file.Files.newInputStream(java.nio.file.Paths.get(debug));
          } catch (Exception e) {
            throw new RuntimeException(e);
          }
        }
        reader = new java.io.BufferedReader(new java.io.InputStreamReader(is), 32768);
        solve();
        out.flush();
        tr((System.currentTimeMillis() - start) + "ms");
      }
    }, "", 64000000).start();
  }

  private static java.io.InputStream is = System.in;
  private static java.io.PrintWriter out = new java.io.PrintWriter(System.out);
  private static java.util.StringTokenizer tokenizer = null;
  private static java.io.BufferedReader reader;

  public static String next() {
    while (tokenizer == null || !tokenizer.hasMoreTokens()) {
      try {
        tokenizer = new java.util.StringTokenizer(reader.readLine());
      } catch (Exception e) {
        throw new RuntimeException(e);
      }
    }
    return tokenizer.nextToken();
  }

  private static double nd() {
    return Double.parseDouble(next());
  }

  private static long nl() {
    return Long.parseLong(next());
  }

  private static int[] na(int n) {
    int[] a = new int[n];
    for (int i = 0; i < n; i++)
      a[i] = ni();
    return a;
  }

  private static char[] ns() {
    return next().toCharArray();
  }

  private static long[] nal(int n) {
    long[] a = new long[n];
    for (int i = 0; i < n; i++)
      a[i] = nl();
    return a;
  }

  private static int[][] ntable(int n, int m) {
    int[][] table = new int[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        table[i][j] = ni();
      }
    }
    return table;
  }

  private static int[][] nlist(int n, int m) {
    int[][] table = new int[m][n];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        table[j][i] = ni();
      }
    }
    return table;
  }

  private static int ni() {
    return Integer.parseInt(next());
  }

  private static void tr(Object... o) {
    if (is != System.in)
      System.out.println(java.util.Arrays.deepToString(o));
  }
}