You are given an array a_1, a_2, ... , a_n and two integers m and k.

You can choose some subarray a_l, a_{l+1}, ..., a_{r-1}, a_r. 

The cost of subarray a_l, a_{l+1}, ..., a_{r-1}, a_r is equal to ∑_{i=l}^{r} a_i - k ⌈ (r - l + 1)/(m) ⌉, where ⌈ x ⌉ is the least integer greater than or equal to x. 

The cost of empty subarray is equal to zero.

For example, if m = 3, k = 10 and a = [2, -4, 15, -3, 4, 8, 3], then the cost of some subarrays are:

  * a_3 ... a_3: 15 - k ⌈ 1/3 ⌉ = 15 - 10 = 5; 
  * a_3 ... a_4: (15 - 3) - k ⌈ 2/3 ⌉ = 12 - 10 = 2; 
  * a_3 ... a_5: (15 - 3 + 4) - k ⌈ 3/3 ⌉ = 16 - 10 = 6; 
  * a_3 ... a_6: (15 - 3 + 4 + 8) - k ⌈ 4/3 ⌉ = 24 - 20 = 4; 
  * a_3 ... a_7: (15 - 3 + 4 + 8 + 3) - k ⌈ 5/3 ⌉ = 27 - 20 = 7. 



Your task is to find the maximum cost of some subarray (possibly empty) of array a.

Input

The first line contains three integers n, m, and k (1 ≤ n ≤ 3 ⋅ 10^5, 1 ≤ m ≤ 10, 1 ≤ k ≤ 10^9).

The second line contains n integers a_1, a_2, ..., a_n (-10^9 ≤ a_i ≤ 10^9).

Output

Print the maximum cost of some subarray of array a.

Examples

Input


7 3 10
2 -4 15 -3 4 8 3


Output


7


Input


5 2 1000
-13 -4 -9 -20 -11


Output


0
import java.io.*;
import java.math.*;
import java.util.*;

import static java.lang.Math.*;
import static java.util.Arrays.*;
import static java.util.Collections.*;
import static java.util.Comparator.*;

public class Main {
    FastScanner in;
    PrintWriter out;
    boolean multitests = false;
    long mod = 998_244_353L; // (long) 1e9 + 7 || (long) 1e9 + 9
    ArrayList<Integer>[] graph;
    ArrayList<GraphPair>[] weightedGraph;

    private void solve() throws IOException {
        // solveA();
        // solveB();
        // solveC();
        solveD();
        // solveE();
        // solveF();
    }

    private void solveA() throws IOException {
        int n = in.nextInt();
        int[] a = in.nextIntArray(n);
        int max1 = max(a[0], a[1]), max2 = min(a[0], a[1]);
        for (int i = 2; i < n; i++) {
            if (a[i] > max1) {
                max2 = max1;
                max1 = a[i];
            } else if (a[i] > max2) {
                max2 = a[i];
            }
        }
        out.println(min(n - 2, min(max1, max2) - 1));
    }

    private void solveB() throws IOException {
        int n = in.nextInt();
        int[] a = in.nextIntArray(n);
        int maxId = 0;
        for (int i = 1; i < n; i++)
            if (a[i] > a[maxId])
                maxId = i;

        int prev = a[maxId];
        int l = maxId - 1, r = maxId + 1;
        while (l >= 0 || r < n) {
            if (l < 0 || (r < n && a[l] < a[r])) {
                if (a[r] < prev) {
                    prev = a[r++];
                } else
                    break;
            } else if (r >= n || (l >= 0 && a[l] > a[r])) {
                if (a[l] < prev) {
                    prev = a[l--];
                } else
                    break;
            } else
                break;
        }
        out.println(l < 0 && r >= n ? "YES" : "NO");
    }

    private void solveC() throws IOException {
        int n = in.nextInt(), k = in.nextInt();
        int[] a = in.nextIntArray(n);
        int[] b = new int[n - 1];
        for (int i = 0; i < n - 1; i++)
            b[i] = a[i + 1] - a[i];
        shuffleInt(b);
        sort(b);
        long ans = 0;
        for (int i = 0; i < n - k; i++)
            ans += b[i];
        out.println(ans);
    }

    private void solveD() throws IOException {
        int n = in.nextInt(), m = in.nextInt();
        long K = in.nextLong();
        long[] a = in.nextLongArray(n);
        long[] suffSum = new long[n];
        for (int i = n - 1; i >= 0; i--)
            suffSum[i] = a[i] + (i + 1 < n ? suffSum[i + 1] : 0);
        // out.println(Arrays.toString(suffSum));

        long ans = 0;
        for (int first = 0; first < min(n, m); first++) {
            int len = 1 + (n - (first + 1)) / m;
            long[] b = new long[len];
            int i = first;
            for (int j = 0; j < len; j++, i += m) {
                //out.print(i + "|");
                b[j] = Long.MIN_VALUE;
                for (int k = max(0, i - m + 1); k <= i; k++) {
                    b[j] = max(b[j], suffSum[k]);
                }
                b[j] -= K;
            }
            //out.println();

            long del = 0;
            for (int j = i - m + 1; j < n; j++)
                del += a[j];
            for (int j = 0; j < len; j++)
                b[j] -= del;
            //for (int j = 0; j < len; j++)
            //out.print(b[j] + " ");
            //out.println();

            long max = Long.MIN_VALUE + K;
            i = first;
            //out.flush();
            long pdel = del;
            for (int j = 0; j < len; j++, i += m) {
                max = max(max - K, b[j]);
                del = i + 1 < n ? (suffSum[i + 1] - pdel) : 0;
                ans = max(ans, max - del);
            }

        }

        out.println(ans);
    }

    private void solveE() throws IOException {

    }

    private void solveF() throws IOException {

    }

    void shuffleInt(int[] a) {
        Random random = new Random();
        for (int i = a.length - 1; i > 0; i--) {
            int j = random.nextInt(i + 1);
            int swap = a[j];
            a[j] = a[i];
            a[i] = swap;
        }
    }

    void shuffleLong(long[] a) {
        Random random = new Random();
        for (int i = a.length - 1; i > 0; i--) {
            int j = random.nextInt(i + 1);
            long swap = a[j];
            a[j] = a[i];
            a[i] = swap;
        }
    }

    void reverseInt(int[] a) {
        for (int i = 0, j = a.length - 1; i < j; i++, j--) {
            int swap = a[i];
            a[i] = a[j];
            a[j] = swap;
        }
    }

    void reverseLong(long[] a) {
        for (int i = 0, j = a.length - 1; i < j; i++, j--) {
            long swap = a[i];
            a[i] = a[j];
            a[j] = swap;
        }
    }

    int maxInt(int[] a) {
        int max = a[0];
        for (int i = 1; i < a.length; i++)
            if (max < a[i])
                max = a[i];
        return max;
    }

    long maxLong(long[] a) {
        long max = a[0];
        for (int i = 1; i < a.length; i++)
            if (max < a[i])
                max = a[i];
        return max;
    }

    int minInt(int[] a) {
        int min = a[0];
        for (int i = 1; i < a.length; i++)
            if (min > a[i])
                min = a[i];
        return min;
    }

    long minLong(long[] a) {
        long min = a[0];
        for (int i = 1; i < a.length; i++)
            if (min > a[i])
                min = a[i];
        return min;
    }

    long sumInt(int[] a) {
        long s = 0;
        for (int i = 0; i < a.length; i++)
            s += a[i];
        return s;
    }

    long sumLong(long[] a) {
        long s = 0;
        for (int i = 0; i < a.length; i++)
            s += a[i];
        return s;
    }

    long gcd(long a, long b) {
        return b == 0 ? a : gcd(b, a % b);
    }

    long binpowmod(long a, long n) {
        long res = 1;
        a %= mod;
        n %= mod - 1;
        while (n > 0) {
            if (n % 2 == 1)
                res = (res * a) % mod;
            a = (a * a) % mod;
            n /= 2;
        }
        return res;
    }

    class GraphPair implements Comparable<GraphPair> {
        int v;
        long w;

        GraphPair(int v, long w) {
            this.v = v;
            this.w = w;
        }

        public int compareTo(GraphPair o) {
            return w != o.w ? Long.compare(w, o.w) : Integer.compare(v, o.v);
        }
    }

    ArrayList<Integer>[] createGraph(int n) throws IOException {
        ArrayList<Integer>[] graph = new ArrayList[n];
        for (int i = 0; i < n; i++)
            graph[i] = new ArrayList<>();
        return graph;
    }

    ArrayList<GraphPair>[] createWeightedGraph(int n) throws IOException {
        ArrayList<GraphPair>[] graph = new ArrayList[n];
        for (int i = 0; i < n; i++)
            graph[i] = new ArrayList<>();
        return graph;
    }

    class FastScanner {
        StringTokenizer st;
        BufferedReader br;

        FastScanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s), 32768);
        }

        String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

        boolean hasNext() throws IOException {
            return br.ready() || (st != null && st.hasMoreTokens());
        }

        int nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        int[] nextIntArray(int n) throws IOException {
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = in.nextInt();
            return a;
        }

        int[][] nextIntTable(int n, int m) throws IOException {
            int[][] a = new int[n][m];
            for (int i = 0; i < n; i++)
                for (int j = 0; j < m; j++)
                    a[i][j] = in.nextInt();
            return a;
        }

        long nextLong() throws IOException {
            return Long.parseLong(next());
        }

        long[] nextLongArray(int n) throws IOException {
            long[] a = new long[n];
            for (int i = 0; i < n; i++)
                a[i] = in.nextLong();
            return a;
        }

        long[][] nextLongTable(int n, int m) throws IOException {
            long[][] a = new long[n][m];
            for (int i = 0; i < n; i++)
                for (int j = 0; j < m; j++)
                    a[i][j] = in.nextLong();
            return a;
        }

        ArrayList<Integer>[] nextGraph(int n, int m, boolean directed) throws IOException {
            ArrayList<Integer>[] graph = createGraph(n);
            for (int i = 0; i < m; i++) {
                int v = in.nextInt() - 1, u = in.nextInt() - 1;
                graph[v].add(u);
                if (!directed)
                    graph[u].add(v);
            }
            return graph;
        }

        ArrayList<GraphPair>[] nextWeightedGraph(int n, int m, boolean directed) throws IOException {
            ArrayList<GraphPair>[] graph = createWeightedGraph(n);
            for (int i = 0; i < m; i++) {
                int v = in.nextInt() - 1, u = in.nextInt() - 1;
                long w = in.nextLong();
                graph[v].add(new GraphPair(u, w));
                if (!directed)
                    graph[u].add(new GraphPair(v, w));
            }
            return graph;
        }

        double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }

        String nextLine() throws IOException {
            return br.readLine();
        }

        boolean hasNextLine() throws IOException {
            return br.ready();
        }
    }

    private void run() throws IOException {
        in = new FastScanner(System.in); // new FastScanner(new FileInputStream(".in"));
        out = new PrintWriter(System.out); // new PrintWriter(new FileOutputStream(".out"));

        for (int t = multitests ? in.nextInt() : 1; t-- > 0; )
            solve();

        out.flush();
        out.close();
    }

    public static void main(String[] args) throws IOException {
        new Main().run();
    }
}