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.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Jialin Ouyang (Jialin.Ouyang@gmail.com)
 */
public class Main {
  public static void main(String[] args) {
    InputStream inputStream = System.in;
    OutputStream outputStream = System.out;
    QuickScanner in = new QuickScanner(inputStream);
    QuickWriter out = new QuickWriter(outputStream);
    TaskD solver = new TaskD();
    solver.solve(1, in, out);
    out.close();
  }

  static class TaskD {
    int a;
    int b;
    int k;
    int T;
    int k2;
    int n;
    int[][] dp;

    public void solve(int testNumber, QuickScanner in, QuickWriter out) {
      a = in.nextInt();
      b = in.nextInt();
      k = in.nextInt();
      k2 = k << 1;
      T = in.nextInt();
      n = (k * T << 1) | 1;
      dp = new int[2][n];
      int t = 0;
      dp[t][0] = 1;
      for (int i = 0; i < T; ++i) {
        for (int j = 1; j < n; ++j) dp[t][j] = IntUtils.add(dp[t][j], dp[t][j - 1]);
        for (int j = 0; j < n; ++j) dp[t ^ 1][j] = IntUtils.sub(dp[t][j], j >= k2 + 1 ? dp[t][j - k2 - 1] : 0);
        t ^= 1;
      }
      int[] sum = new int[n];
      for (int i = 0; i < n; ++i) {
        sum[i] = IntUtils.add(dp[t][i], i > 0 ? sum[i - 1] : 0);
      }
      int res = 0;
      for (int i = 0; i < n; ++i) {
        res = IntUtils.add(res, i + a >= b + 1 ? IntUtils.mul(dp[t][i], sum[Math.min(i + a - b - 1, n - 1)]) : 0);
      }
      out.println(res);
    }

  }

  static class IntUtils {
    public static int MOD = 1000000007;

    public static int add(int a, int b) {
      return add(a, b, MOD);
    }

    public static int add(int a, int b, int mod) {
      return slightFix(a + b, mod);
    }

    public static int sub(int a, int b) {
      return sub(a, b, MOD);
    }

    public static int sub(int a, int b, int mod) {
      return slightFix(a - b, mod);
    }

    public static int mul(int a, int b) {
      return mul(a, b, MOD);
    }

    public static int mul(int a, int b, int mod) {
      return a > 0
          ? (b < mod / a
          ? a * b
          : (int) ((long) a * b % mod))
          : 0;
    }

    private static int slightFix(int a, int mod) {
      return a >= mod
          ? a - mod
          : a < 0
          ? a + mod
          : a;
    }

  }

  static class QuickScanner {
    private static final int BUFFER_SIZE = 1024;
    private InputStream stream;
    private byte[] buffer;
    private int currentPostion;
    private int numberOfChars;

    public QuickScanner(InputStream stream) {
      this.stream = stream;
      this.buffer = new byte[BUFFER_SIZE];
      this.currentPostion = 0;
      this.numberOfChars = 0;
    }

    public int nextInt() {
      int c = nextNonSpaceChar();
      boolean positive = true;
      if (c == '-') {
        positive = false;
        c = nextChar();
      }
      int res = 0;
      do {
        if (c < '0' || '9' < c) throw new RuntimeException();
        res = res * 10 + c - '0';
        c = nextChar();
      } while (!isSpaceChar(c));
      return positive ? res : -res;
    }

    public int nextNonSpaceChar() {
      int res = nextChar();
      for (; isSpaceChar(res) || res < 0; res = nextChar()) ;
      return res;
    }

    public int nextChar() {
      if (numberOfChars == -1) {
        throw new RuntimeException();
      }
      if (currentPostion >= numberOfChars) {
        currentPostion = 0;
        try {
          numberOfChars = stream.read(buffer);
        } catch (Exception e) {
          throw new RuntimeException(e);
        }
        if (numberOfChars <= 0) {
          return -1;
        }
      }
      return buffer[currentPostion++];
    }

    public boolean isSpaceChar(int c) {
      return c == ' '
          || c == '\n'
          || c == '\r'
          || c == '\t'
          || c < 0;
    }

  }

  static class QuickWriter {
    private final PrintWriter writer;

    public QuickWriter(OutputStream outputStream) {
      this.writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
    }

    public QuickWriter(Writer writer) {
      this.writer = new PrintWriter(writer);
    }

    public void print(Object... objects) {
      for (int i = 0; i < objects.length; ++i) {
        if (i > 0) {
          writer.print(' ');
        }
        writer.print(objects[i]);
      }
    }

    public void println(Object... objects) {
      print(objects);
      writer.print('\n');
    }

    public void close() {
      writer.close();
    }

  }
}

