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.io.*;
import java.math.*;
 
public class Main {
    static PrintWriter out;
    static Reader in;
    public static void main(String[] args) throws IOException {
        //out = new PrintWriter(new File("out.txt"));
        //PrintWriter out = new PrintWriter(System.out);
        //in = new Reader(new FileInputStream("in.txt"));
        //Reader in = new Reader();
        input_output();
        Main solver = new Main();
        solver.solve();
        out.flush();
        out.close();
 
    }
 
    static long INF = (long)1e15+5;
    static int maxn = (int)2e5+1000;
    static int mod=(int)1e9+7 ;
    static int n, m, q, k, t;

    void solve() throws IOException{
        int a = in.nextInt(),
            b = in.nextInt();
        k = in.nextInt();
        t = in.nextInt();

        int[][] dif = new int[2][maxn];
        int offset = 1000*100;

        dif[0][offset+a] = 1;
        for (int i = 1; i <= t; i++) {
            for (int j = 0; j < maxn; j++) {
                if (dif[0][j] == 0) continue;
                dif[1][j-k] = mod(dif[1][j-k], dif[0][j]);
                dif[1][j+k+1] = mod(dif[1][j+k+1], -dif[0][j]);
            }

            for (int j = 1; j < maxn; j++) {
                dif[1][j] = mod(dif[1][j], dif[1][j-1]);
                dif[0][j] = dif[1][j];
            }
            for (int j = 0; j < maxn; j++) dif[1][j] = 0;
        }

        int[][] dif2 = new int[2][maxn];

        dif2[0][offset+b] = 1;
        for (int i = 1; i <= t; i++) {
            for (int j = 0; j < maxn; j++) {
                if (dif2[0][j] == 0) continue;
                dif2[1][j-k] = mod(dif2[1][j-k], dif2[0][j]);
                dif2[1][j+k+1] = mod(dif2[1][j+k+1], -dif2[0][j]);
            }

            for (int j = 1; j < maxn; j++) {
                dif2[1][j] = mod(dif2[1][j], dif2[1][j-1]);
                dif2[0][j] = dif2[1][j];
            }
            for (int j = 0; j < maxn; j++) dif2[1][j] = 0;
        }


        int ans = 0, sum = 0;
        sum = dif2[0][0];
        for (int i = 1; i < maxn; i++) {
            ans = mod(ans, (int)(((long)sum*dif[0][i])%mod));
            sum = mod(sum, dif2[0][i]);
        }

        out.println(ans);
    }  

    //<>

    static int mod(int a, int b) {
        if (a+b >= mod) return a+b-mod;
        else if (a+b < 0) return a+b+mod;
        return a+b;
    }


    static class Reader {
 
        private InputStream mIs;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
    
        public Reader() {
            this(System.in);
        }
    
        public Reader(InputStream is) {
            mIs = is;
        }
    
        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
    
        }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = mIs.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }
    
        public String nextLine() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isEndOfLine(c));
            return res.toString();
        }
    
        public String next() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }
    
        double nextDouble()
        {
            return Double.parseDouble(next());
        }
    
        public long nextLong() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }
    
        public int nextInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }
    
        public boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
    
        public boolean isEndOfLine(int c) {
            return c == '\n' || c == '\r' || c == -1;
        }
 
    }
    static void input_output() throws IOException {
        File f = new File("in.txt");
        if(f.exists() && !f.isDirectory()) { 
            in = new Reader(new FileInputStream("in.txt"));
        } else in = new Reader();
        f = new File("out.txt");
        if(f.exists() && !f.isDirectory()) {
            out = new PrintWriter(new File("out.txt"));
        } else out = new PrintWriter(System.out);
    }
}