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.PrintWriter;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;
import java.util.*;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
  public static void main(String[] args) {
    InputStream inputStream = System.in;
    OutputStream outputStream = System.out;
    InputReader in = new InputReader(inputStream);
    PrintWriter out = new PrintWriter(outputStream);
    Task solver = new Task();
    solver.solve(1, in, out);
    out.close();
  }

  static class Task {
    static int N = (int) (2e5 + 1e4);
    static int MOD = (int) (1e9 + 7);
    
    public void solve(int testNumber, InputReader in, PrintWriter out) {
      int a = in.nextInt();
      int b = in.nextInt();
      int k = in.nextInt();
      int t = in.nextInt();
      int lef = N + a - b;
      int rig = N + a - b;
      int[] sum = new int[N * 2 + 1];
      int[] dp = new int[N * 2];
      dp[lef] = 1;
      for (int i = 0; i < t * 2; i++) {
        lef -= k;
        rig += k;
        sum[lef - k] = 0;
        for (int j = lef - k; j <= rig + k; j++) {
          sum[j + 1] = sum[j] + dp[j];
          if (sum[j + 1] >= MOD) sum[j + 1] -= MOD;
        }
        for (int j = lef; j <= rig; j++) {
          dp[j] = sum[j + k + 1] - sum[j - k];
          if (dp[j] < 0) dp[j] += MOD;
        }
      }
      int ans = 0;
      for (int i = N + 1; i <= rig; i++) {
        ans += dp[i];
        if (ans >= MOD) ans -= MOD;
      }
      out.println(ans);
    }
    
  }

  static class InputReader {
    public BufferedReader reader;
    public StringTokenizer tokenizer;

    public InputReader(InputStream stream) {
      reader = new BufferedReader(new InputStreamReader(stream), 32768);
      tokenizer = null;
    }

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

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

  }
}