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.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
 */
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) {
            final int MOD = 1000000007;
            int a = in.nextInt(), b = in.nextInt(), k = in.nextInt(), t = in.nextInt();
            int n = 2 * t * k, ans = 0;
            int[][] f = new int[t + 1][n + 1], dp = new int[t + 1][n + 1];
            f[0][0] = 1;
            for (int j = 0; j <= n; j++) {
                dp[0][j] = 1;
            }
            for (int i = 1; i <= t; i++) {
                for (int j = 0; j <= n; j++) {
                    f[i][j] = dp[i - 1][j];
                    if (j - 2 * k - 1 >= 0) {
                        f[i][j] -= dp[i - 1][j - 2 * k - 1];
                        f[i][j] %= MOD;
                    }
                }
                dp[i][0] = f[i][0];
                for (int j = 1; j <= n; j++) {
                    dp[i][j] = dp[i][j - 1] + f[i][j];
                    dp[i][j] %= MOD;
                }
            }
//        for (int i = 0; i <= t; i++) {
//            for (int j = 0; j <= n; j++) {
//                out.print(f[i][j] + " ");
//            }
//            out.println();
//        }
//        out.println();
//        for (int i = 0; i <= t; i++) {
//            for (int j = 0; j <= n; j++) {
//                out.print(dp[i][j] + " ");
//            }
//            out.println();
//        }
            for (int i = 0; i <= n; i++) {
                if (a - b + i - 1 >= 0) {
                    ans += (1L * f[t][i] * dp[t][Math.min(a - b + i - 1, n)]) % MOD;
                    ans %= MOD;
                }
            }
            out.println(Math.floorMod(ans, MOD));
        }

    }

    static class InputReader {
        private BufferedReader br;
        private StringTokenizer st;

        public InputReader(InputStream stream) {
            br = new BufferedReader(new InputStreamReader(stream), 32768);
            st = null;
        }

        public String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return st.nextToken();
        }

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

    }
}

