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.io.PrintStream;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Wolfgang Beyer
 */
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);
        TaskD solver = new TaskD();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskD {
        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();
            //long[][] dp = new long[2][404001];
            long[][] dp = new long[2][500000];

            int mod = 1000000007;

        /*for (int j = 0; j < 2; j++) {
            for (int i = 0; i < 404001; i++) dp[j][i] = 0;
        }*/

            //int shift = 202000;
            int shift = 250000;

            int current = 0;
            dp[current][shift] = 1;
            for (int i = 1; i <= t; i++) {
                current ^= 1;
                long sumToAdd = 0;
                long sumToSubstract = 0;
                for (int j = -i * 2 * k; j <= i * 2 * k; j++) {
                    sumToAdd += -dp[current ^ 1][j - 1 + shift] + dp[current ^ 1][j + 2 * k + shift];
                    sumToAdd = sumToAdd % mod;
                    //sumToAdd = ((sumToAdd % mod) + mod) % mod;
                    sumToSubstract += dp[(current ^ 1)][j - 1 + shift] - dp[current ^ 1][j - 2 * k - 2 + shift];
                    //sumToSubstract = ((sumToSubstract % mod) + mod) % mod;
                    sumToSubstract = sumToSubstract % mod;
                    dp[current][j + shift] = dp[current][j - 1 + shift] + sumToAdd - sumToSubstract;
                    //dp[current][j + shift] = ((dp[current][j + shift] % mod) + mod) % mod;
                    dp[current][j + shift] = dp[current][j + shift] % mod;
                }
            }
            long result = 0;
            for (int i = b - a + 1; i <= 2 * k * t; i++) {
                result += dp[current][i + shift];
                result = ((result % mod) + mod) % mod;
                //result = result % mod;
            }
            out.println(result);
        }

    }

    static class InputReader {
        private static BufferedReader in;
        private static StringTokenizer tok;

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

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

        public String next() {
            try {
                while (tok == null || !tok.hasMoreTokens()) {
                    tok = new StringTokenizer(in.readLine());
                }
            } catch (IOException ex) {
                System.err.println("An IOException was caught :" + ex.getMessage());
            }
            return tok.nextToken();
        }

    }
}

