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
 *
 * @author FinnTheHuman
 */
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 {
        static final int mod = 1000000007;
        static final int sumCount = 410000 + 9;
        static final int zero = sumCount / 2;
        int a;
        int b;
        int k;
        int t;

        int modulo(int a, int b) {
            return ((a % b) + b) % b;
        }

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            a = in.nextInt();
            b = in.nextInt();
            k = in.nextInt();
            t = in.nextInt();
            int[][] dp = new int[2][sumCount];
            int cur = 1, prev = 0;
            dp[prev][a + zero - b] = 1;
            for (int iteration = 0; iteration < 2 * t; ++iteration) {
                for (int i = 0; i < sumCount; ++i) {
                    if (!(i - k - 1 < 0 || i + k >= sumCount || dp[prev][i + k] + dp[prev][i - k - 1] == 0)) {
                        dp[cur][i] = modulo(dp[prev][i + k] - dp[prev][i - k - 1], mod);
                    }
                    if (i > 0) {
                        dp[cur][i] += dp[cur][i - 1];
                        dp[cur][i] %= mod;
                    }
                }
                cur = 1 - cur;
                prev = 1 - prev;
            }
            int ret = 0;
            for (int i = zero + 1; i < sumCount; ++i) {
                ret += dp[prev][i];
                ret %= mod;
            }
            out.println(ret);
        }

    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 65536 / 2);
            tokenizer = null;
        }

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

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

    }
}

