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.*;
import java.util.*;
import java.math.*;

public class Solve3 {

  static long MOD = 1000000007L;
  static long add(long a, long b) {
    return (a + b + MOD) % MOD;
  }
  static long times(long a, long b) {
    return (a * b) % MOD;
  }
  public static void main(String[] args) {
	MyScanner scanner = new MyScanner();
	PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
	
    int a = scanner.nextInt();
	int b = scanner.nextInt();
	int k = scanner.nextInt();
	int t = scanner.nextInt();
	int size = 500000;
	long tab[] = new long[size];
	long all[] = new long[size];
	long help[] = new long[size];
	int ZERO = size/2;
	for(int i = ZERO - k; i <= ZERO + k; i++)
	  tab[i] = 1;
	for(int it = 1; it < t; it++) {
	  Arrays.fill(help, 0L);
	  long sum = 0;
	  for(int i = ZERO - k - t * k; i <= ZERO + k - t * k; i++)
	    sum = add(sum, tab[i]);
	  for(int i = ZERO - k * t; i <= ZERO + k * t; i++) {
	    help[i] = sum;
		sum = add(sum, -tab[i-k]);
		sum = add(sum, tab[i+k+1]);
	  }
	  for(int i = 0; i < size; i++)
	    tab[i] = help[i];
	}
    for(int i = 0; i < size-1; i++)
	  all[i+1] = add(all[i], tab[i+1]);
	long res = 0;
	for(int i = ZERO - k * t; i <= ZERO + k * t; i++) {
	 // System.out.println(i - ZERO + " " + all[i-1+a-b] + " " + tab[i]);
	  res = add(res, times(all[i-1+a-b], tab[i]));
	}
	out.println(res);
	out.close();
  }

  public static class MyScanner {
      BufferedReader br;
      StringTokenizer st;
 
      public MyScanner() {
         br = new BufferedReader(new InputStreamReader(System.in));
      }
 
      String next() {
          while (st == null || !st.hasMoreElements()) {
              try {
                  st = new StringTokenizer(br.readLine());
              } catch (IOException e) {
                  e.printStackTrace();
              }
          }
          return st.nextToken();
      }
 
      int nextInt() {
          return Integer.parseInt(next());
      }
 
      long nextLong() {
          return Long.parseLong(next());
      }
 
      double nextDouble() {
          return Double.parseDouble(next());
      }
 
      String nextLine(){
          String str = "";
	  try {
	     str = br.readLine();
	  } catch (IOException e) {
	     e.printStackTrace();
	  }
	  return str;
      }

   }
}