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.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;

/**
 * Created by BananaTree on 16-9-18.
 * email: intfloat@pku.edu.cn
 */
public class D {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskA solver = new TaskA();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskA {

        private static final int MOD = 1000000007;

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int a = in.nextInt(), b = in.nextInt();
            int k = in.nextInt(), t = in.nextInt();
            int[] cnt1 = calculate(a, k, t);
            int[] cnt2 = calculate(b, k, t);
            for (int i = cnt1.length - 1; i > 0; --i) {
                cnt1[i] = (cnt1[i] - cnt1[i - 1]) % MOD;
                if (cnt1[i] < 0) {
                    cnt1[i] = (cnt1[i] + MOD) % MOD;
                }
            }
            int res = 0;
            for (int i = 1; i < cnt1.length; ++i) {
                int pos = Math.min(cnt2.length - 1, i - 1);
                long val = (long)cnt1[i] * (long)cnt2[pos];
                val %= MOD;
                res = (res + (int)val) % MOD;
            }
            out.println(res);
        }

        private int[] calculate(int start, int k, int t) {
            int mx = start + 2 * k * t;
            int[][] dp = new int[2][mx + 1];
            for (int i = start; i <= mx; ++i) {
                dp[0][i] = 1;
            }
            for (int i = 1; i <= t; ++i) {
                int pv = (i - 1) % 2, cur = 1 - pv;
                for (int j = 0; j <= mx; ++j) {
                    dp[cur][j] = dp[pv][j];
                    if (j - 2 * k - 1 >= 0) {
                        dp[cur][j] -= dp[pv][j - 2 * k - 1];
                    }
                    dp[cur][j] %= MOD;
                    if (dp[cur][j] < 0) {
                        dp[cur][j] = (dp[cur][j] + MOD) % MOD;
                    }
                }
                for (int j = 1; j <= mx; ++j) {
                    dp[cur][j] += dp[cur][j - 1];
                    dp[cur][j] %= MOD;
                }
            }
            return dp[t % 2];
        }

    }

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

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            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());
        }

    }
}

