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

public class Main {
	static int MOD=1000000007;
	
	public static void main(String[] args) throws FileNotFoundException {
		InputReader in=new InputReader(System.in);
		PrintWriter out=new PrintWriter(System.out);
		//Scanner in=new Scanner(System.in);
		
		int a=in.nextInt();
		int b=in.nextInt();
		int k=in.nextInt();
		int n=in.nextInt();
		k=2*k;
		int[] d=new int[n*k+1];
		int[] sum=new int[n*k+1];
		for(int i=1;i<=n;i++){
			if(i==1){
				for(int j=0;j<=k;j++){
					d[j]=1;
				}
			}
			else{
				for(int j=k*i;j>0;j--){
					if(j>k){
						d[j]=(sum[j]-sum[j-k-1])%MOD;
					}
					else{
						d[j]=sum[j];
					}
				}
			}
			sum[0]=1;
			for(int j=1;j<=n*k;j++){
				sum[j]=(sum[j-1]+d[j])%MOD;
			}
		}
		int diff=b-a;
		int ans=0;
		for(int j=0;j<=n*k;j++){
			if(j<=diff){
				continue;
			}
			int u=Math.min(j-diff-1,n*k);
			ans=(int)((ans+(long)d[j]*sum[u])%MOD);
		}
		ans=(ans+MOD)%MOD;
		System.out.println(ans);
		
		out.close();
	}
	
	static class InputReader {
		BufferedReader br;
		StringTokenizer st;

		public InputReader (File f){
			try{
				br=new BufferedReader(new FileReader(f));
			}catch(FileNotFoundException e){
				e.printStackTrace();
			}
		}

		public InputReader (InputStream in){
			br=new BufferedReader(new InputStreamReader(in));
		}

		public String next(){
			while(st==null||!st.hasMoreTokens()){
				try{
					st=new StringTokenizer(br.readLine());
				}catch(IOException e){
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}
		
		public boolean hasNext(){
			while(st==null||!st.hasMoreTokens()){
				String s=null;
				try{
					s=br.readLine();
				}catch(IOException e){
					e.printStackTrace();
				}
				if(s==null)
					return false;
				st=new StringTokenizer(s);
			}
			return true;
		}

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

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

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