The on-board computer on Polycarp's car measured that the car speed at the beginning of some section of the path equals v1 meters per second, and in the end it is v2 meters per second. We know that this section of the route took exactly t seconds to pass.

Assuming that at each of the seconds the speed is constant, and between seconds the speed can change at most by d meters per second in absolute value (i.e., the difference in the speed of any two adjacent seconds does not exceed d in absolute value), find the maximum possible length of the path section in meters.

Input

The first line contains two integers v1 and v2 (1 ≤ v1, v2 ≤ 100) — the speeds in meters per second at the beginning of the segment and at the end of the segment, respectively.

The second line contains two integers t (2 ≤ t ≤ 100) — the time when the car moves along the segment in seconds, d (0 ≤ d ≤ 10) — the maximum value of the speed change between adjacent seconds.

It is guaranteed that there is a way to complete the segment so that:

  * the speed in the first second equals v1, 
  * the speed in the last second equals v2, 
  * the absolute value of difference of speeds between any two adjacent seconds doesn't exceed d. 

Output

Print the maximum possible length of the path segment in meters. 

Examples

Input

5 6
4 2


Output

26

Input

10 10
10 0


Output

100

Note

In the first sample the sequence of speeds of Polycarpus' car can look as follows: 5, 7, 8, 6. Thus, the total path is 5 + 7 + 8 + 6 = 26 meters.

In the second sample, as d = 0, the car covers the whole segment at constant speed v = 10. In t = 10 seconds it covers the distance of 100 meters.
import java.awt.Point;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.text.DecimalFormat;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Set;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;


public class Main {
    static Main.MyScanner sc = new Main.MyScanner();
    // static Main.Parser sc = new Parser(System.in);
    static PrintWriter out = new PrintWriter(System.out, true);

    public static void main(String[] args) throws Exception {
        int s = sc.nextInt(),e = sc.nextInt(),n = sc.nextInt(),d = sc.nextInt(),arr[] = new int[n];
        arr[0] = s;arr[n-1] = e;
        for(int i = 1 ; i < n-1 ; i++) arr[i] = arr[i-1] + d ;
        for(int i = n-2 ; i > 0 ; i-- ){
            if(Math.abs(arr[i]-arr[i+1]) > d ){
                arr[i] = arr[i+1] + d ;
            }else
                break;
        }
        int tot = 0 ;
        for(int x : arr) tot += x ;
        
        out.println(tot);
        
        out.close();
    }

    private static int[] get(int[][] arr, int[] qus) {
        // TODO Auto-generated method stub
        int ans[] = new int[arr.length];
        Arrays.sort(qus);
        for(int i = 0 ; i < arr.length ; i++){
//          System.out.println(Arrays.toString(arr[i])+" "+Arrays.toString(qus));
            int count = 0 ;
            for(int j = 0,k = 0 ; j < arr[i].length && k < qus.length ; ){
                if(arr[i][j] == qus[k]){
                    count++;
                    j++;k++;
                }else if(arr[i][j] < qus[k]){
                    j++;
                }else
                    k++;
            }
            ans[i] = count;
//          System.out.println(count);
        }
        return ans;
    }

    public int lengthOfLongestSubstring(String s) {
        int pos = 0,ans = 0;
        HashMap<Character,Integer> hm = new HashMap<Character, Integer>();
        for(int i = 0 ; i < s.length() ; i++){
            if(hm.containsKey(s.charAt(i)) && pos <= hm.get(s.charAt(i))){
                ans = Math.max(ans, i-pos);
                pos = hm.get(s.charAt(i))+1;
            }
            hm.put(s.charAt(i), i);
        }
        ans = Math.max(ans, s.length() - pos);
        return ans;
    }

    static private class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        public int mod(long x) {
            return (int) x % 1000000007;
        }

        public int mod(int x) {
            return x % 1000000007;
        }

        boolean hasNext() {
            if (st.hasMoreElements())
                return true;
            try {
                st = new StringTokenizer(br.readLine());
            } catch (IOException e) {
                e.printStackTrace();
            }
            return st.hasMoreTokens();
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (Exception e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

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

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

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

    static class Parser {
        final private int BUFFER_SIZE = 65536; // 2^16, a good compromise for
                                                // some problems
        private InputStream din; // Underlying input stream
        private byte[] buffer; // Self-maintained buffer
        private int bufferPointer; // Current read position in the buffer
        private int bytesRead; // Effective bytes in the buffer read from the
                                // input stream

        public Parser(InputStream in) {
            din = in;
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        /**
         * Read the next integer from the input stream.
         * 
         * @return The next integer.
         * @throws IOException
         */
        public int nextInt() throws IOException {
            int result = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            while (c >= '0' && c <= '9') {
                result = result * 10 + c - '0';
                c = read();
            }
            if (neg)
                return -result;
            return result;
        }

        /**
         * Read the next byte of data from the input stream.
         * 
         * @return the next byte of data, or -1 if the end of the stream is
         *         reached.
         * @throws IOException
         *             if an I/O error occurs.
         */
        public byte read() throws IOException {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }

        /**
         * Read data from the input stream into the buffer
         * 
         * @throws IOException
         *             if an I/O error occurs.
         */
        private void fillBuffer() throws IOException {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }
    }
}