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.StringTokenizer;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.io.OutputStream;
public class D {
	public static void main(String args[]) {
		Sc scan = new Sc(System.in);
		int a = scan.nI();
		int b = scan.nI();
		int k = scan.nI();
		int t = scan.nI();
		int max = Math.max(a,b);
        int maxscore = 2*k*t+max+1;
		long[][] Ma = new long[maxscore][t+1];
		Ma[a][0] = 1;
		long[][] Mb = new long[maxscore][t+1];
		Mb[b][0] = 1;
        int points = k*2 + 1;
        long mod = 1000000007L;
		for(int tt = 1; tt<=t; tt++) {
            long summa = 0;
            long summb = 0;
            for(int i = 0; i<points; i++) {
                summa = (summa + Ma[i][tt-1])%mod;
                summb = (summb + Mb[i][tt-1])%mod;
                Ma[i][tt] = summa;
                Mb[i][tt] = summb;
            }
			for(int sc = points; sc<=max + (points-1)*tt; sc++) {
				summa = (mod + summa - Ma[sc-points][tt-1] + Ma[sc][tt-1])%mod;
                summb = (mod + summb - Mb[sc-points][tt-1] + Mb[sc][tt-1])%mod;
                Ma[sc][tt] = summa;
                Mb[sc][tt] = summb;
			}
		}
		long suma[] = new long[maxscore];
		for(int i = maxscore-2; i>=0; i--) {
			suma[i] = (suma[i+1] + Ma[i+1][t])%mod;
		}
		long sum = 0;
		for(int i = 0; i<maxscore; i++) {
			sum = (sum + suma[i]*Mb[i][t])%mod;
		}
		System.out.println(sum);
	}
}
class Sc {
    public Sc(InputStream i) {
        r = new BufferedReader(new InputStreamReader(i));
    }

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

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

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

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

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

    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;
    }
}