Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k, - k + 1, - k + 2, ..., - 2, - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.

Memory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)2t games in total. Since the answer can be very large, you should print it modulo 109 + 7. Please solve this problem for Memory.

Input

The first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.

Output

Print the number of possible games satisfying the conditions modulo 1 000 000 007 (109 + 7) in one line.

Examples

Input

1 2 2 1


Output

6


Input

1 1 1 2


Output

31


Input

2 12 3 1


Output

0

Note

In the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.
import java.math.BigInteger;
import java.util.*;
import java.io.*;

public class Main {
    static IO io;
    static int[][] f = new int[205][400005];

    public static void main(String[] args) throws Exception {

        io = new IO(System.in, System.out);
        solve();
        io.close();
    }

    static void solve() {
        int i, j;
        int a = io.nextInt();
        int b = io.nextInt();
        int k = io.nextInt();
        int t = io.nextInt();

        k <<= 1;
        a = t * k - a + b;
        t <<= 1;
        int p = t * k;
        if (a > p) {
            io.println("0");
            return;
        }
        int MOD = (int) 1e9 + 7;
        //System.out.println("MOD: "+MOD);
        for (i = 0; i <= p; i++) {
            f[0][i] = 1;
        }

        for (i = 1; i <= t; i++)
            for (j = 0; j <= p; j++)
                f[i][j] = (int)
                        (
                                (
                                        (long) F(i, j - 1) + F(i - 1, j) - F(i - 1, j - k - 1)
                                ) % MOD
                        );


        p = (F(t, p) - F(t, a)) % MOD;

        if (p < 0) {
            p += MOD;
        }
        io.println(p);


    }


    static int F(int x, int y) {

        return y < 0 ? 0 : f[x][y];

    }

    static class IO extends PrintWriter {
        public IO(InputStream i, OutputStream o) {
            super(new BufferedOutputStream(o));
            r = new BufferedReader(new InputStreamReader(i));
        }

        @Override
        public void println(String a) {
            synchronized (lock) {
                print(a);
                print('\n');
            }
        }

        public boolean hasMoreTokens() {
            return peekToken() != null;
        }

        public int nextInt() {
            return Integer.parseInt(nextToken());
        }

        public double nextDouble() {
            return Double.parseDouble(nextToken());
        }

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

        public String next() {
            return nextToken();
        }

        public BigInteger nextBigInteger() {
            return new BigInteger(next());
        }

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

        public Integer[] nextIntegerArray(int n) {
            Integer[] a = new Integer[n];
            for (int i = 0; i < n; i++) {
                a[i] = io.nextInt();
            }
            return a;
        }


        private BufferedReader r;
        private String line;
        private StringTokenizer st;
        private String token;

        private String peekToken() {
            if (token == null)
                try {
                    while (st == null || !st.hasMoreTokens()) {
                        line = r.readLine();
                        if (line == null) return null;
                        st = new StringTokenizer(line);
                    }
                    token = st.nextToken();
                } catch (IOException e) {
                }
            return token;
        }

        private String nextToken() {
            String ans = peekToken();
            token = null;
            return ans;
        }
    }
}