Problem: Imagine that you are in a building that has exactly n floors. You can move between the floors in a lift. Let's number the floors from bottom to top with integers from 1 to n. Now you're on the floor number a. You are very bored, so you want to take the lift. Floor number b has a secret lab, the entry is forbidden. However, you already are in the mood and decide to make k consecutive trips in the lift.

Let us suppose that at the moment you are on the floor number x (initially, you were on floor a). For another trip between floors you choose some floor with number y (y ≠ x) and the lift travels to this floor. As you cannot visit floor b with the secret lab, you decided that the distance from the current floor x to the chosen y must be strictly less than the distance from the current floor x to floor b with the secret lab. Formally, it means that the following inequation must fulfill: |x - y| < |x - b|. After the lift successfully transports you to floor y, you write down number y in your notepad.

Your task is to find the number of distinct number sequences that you could have written in the notebook as the result of k trips in the lift. As the sought number of trips can be rather large, find the remainder after dividing the number by 1000000007 (109 + 7).

Input

The first line of the input contains four space-separated integers n, a, b, k (2 ≤ n ≤ 5000, 1 ≤ k ≤ 5000, 1 ≤ a, b ≤ n, a ≠ b).

Output

Print a single integer — the remainder after dividing the sought number of sequences by 1000000007 (109 + 7).

Examples

Input

5 2 4 1


Output

2


Input

5 2 4 2


Output

2


Input

5 3 4 1


Output

0

Note

Two sequences p1, p2, ..., pk and q1, q2, ..., qk are distinct, if there is such integer j (1 ≤ j ≤ k), that pj ≠ qj.

Notes to the samples:

  1. In the first sample after the first trip you are either on floor 1, or on floor 3, because |1 - 2| < |2 - 4| and |3 - 2| < |2 - 4|. 
  2. In the second sample there are two possible sequences: (1, 2); (1, 3). You cannot choose floor 3 for the first trip because in this case no floor can be the floor for the second trip. 
  3. In the third sample there are no sought sequences, because you cannot choose the floor for the first trip. 

Solution (in JAVA):

Solution:


import java.io.*;

public class Main {
    private final Reader reader;

    private final Writer writer;

    public static void main(String[] args) throws IOException {
        new Main().solve();

    }

    private void solve() throws IOException {
        int MOD = 1000000007;
        int N = reader.nextUnsignedInt();
        int A = reader.nextUnsignedInt() - 1;
        int B = reader.nextUnsignedInt() - 1;
        int K = reader.nextUnsignedInt();

        //d[i][j] = in how many ways we can end up on floor i in j trips
        int dp[][] = new int[N][K + 1];

        dp[A][0] = 1;

        for (int k = 1; k <= K; k++) {
            int s1 = 0;
            for (int i = 0; i < B; i++) {
                s1 = sum(s1, dp[i][k - 1], MOD);
            }
            if (B > 0) {
                dp[B - 1][k] = sum(s1, -dp[B - 1][k - 1], MOD);
            }
            if (B > 1) {
                dp[B - 2][k] = sum(dp[B - 1][k], -dp[B - 2][k - 1], MOD);
            }

            int max = B - 2;
            for (int i = B - 3; i >= 0; i--) {
                dp[i][k] = sum(sum(dp[i + 1][k], dp[i + 1][k - 1], MOD), -dp[i][k - 1], MOD);
                if (Math.abs(max - B) <= Math.abs(i - max)) {
                    dp[i][k] = sum(dp[i][k], -dp[max][k - 1], MOD);
                    max--;
                }
            }

            s1 = 0;
            for (int i = B + 1; i < N; i++) {
                s1 = sum(s1, dp[i][k - 1], MOD);
            }

            if (B < N - 1) {
                dp[B + 1][k] = sum(s1, -dp[B + 1][k - 1], MOD);
            }
            if (B < N - 2) {
                dp[B + 2][k] = sum(dp[B + 1][k], -dp[B + 2][k - 1], MOD);
            }
            max = B + 2;
            for (int i = B + 3; i < N; i++) {
                dp[i][k] = sum(sum(dp[i - 1][k], dp[i - 1][k - 1], MOD), -dp[i][k - 1], MOD);
                if (Math.abs(max - B) <= Math.abs(i - max)) {
                    dp[i][k] = sum(dp[i][k], -dp[max][k - 1], MOD);
                    max++;
                }
            }
        }

        int ans = 0;
        for (int i = 0; i < N; i++) {
            ans = sum(ans, dp[i][K], MOD);
        }
        writer.print(ans + "\n");
        writer.flush();
    }

    private int sum(int a, int b, int mod) {
        int ans = a + b;
        if (ans < 0) {
            ans += mod;
        }
        if (ans >= mod) {
            ans -= mod;
        }
        return ans;
    }

    Main(InputStream in, OutputStream out) {
        this.reader = new Reader(in);
        this.writer = new Writer(out);
    }

    public Main() {
        this.reader = new Reader();
        this.writer = new Writer();
    }


}

class Reader {

    private final int BUFFER_SIZE = 65536;

    private final DataInputStream din;

    private final byte[] buffer;

    private int bufferPointer, bytesRead;

    Reader() {
        din = new DataInputStream(System.in);
        buffer = new byte[BUFFER_SIZE];
        bufferPointer = bytesRead = 0;
    }

    public Reader(InputStream in) {
        din = new DataInputStream(in);
        buffer = new byte[BUFFER_SIZE];
        bufferPointer = bytesRead = 0;
    }

    public long nextUnsignedLong() throws IOException {
        long ret = 0;
        byte c = read();
        while (c <= 32) c = read();
        do {
            ret = ret * 10 + c - '0';
        } while ((c = read()) >= '0');
        return ret;
    }

    public int nextUnsignedInt() throws IOException {
        int ret = 0;
        byte c = read();
        while (c <= 32) c = read();
        do {
            ret = ret * 10 + c - '0';
        } while ((c = read()) >= '0');
        return ret;
    }

    public int nextInt() throws IOException {
        int ret = 0;
        byte c = read();
        while (c <= ' ') c = read();
        boolean neg = (c == '-');
        if (neg) {
            c = read();
        }
        do {
            ret = ret * 10 + c - '0';
        } while ((c = read()) >= '0');
        if (neg) {
            return -ret;
        }
        return ret;
    }

    public String nextString(int MAX) throws IOException {
        int cnt = 0;
        char[] buf = new char[MAX];
        byte c;
        while ((c = read()) < 33) ;
        buf[cnt++] = (char) c;
        while ((c = read()) >= 33) {
            buf[cnt++] = (char) c;
        }
        return new String(buf, 0, cnt);
    }

    public char firstCharOfNextUnSpacedString() throws IOException {
        byte c;
        char res;
        while ((c = read()) < 33) ;
        res = (char) c;
        while ((c = read()) >= 33) ;
        return res;
    }

    private void fillBuffer() throws IOException {
        bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
        if (bytesRead == -1) {
            buffer[0] = -1;
        }
    }

    private byte read() throws IOException {
        if (bufferPointer == bytesRead) {
            fillBuffer();
        }
        return buffer[bufferPointer++];
    }
}

class Writer {
    private final BufferedWriter out;

    Writer() {
        out = new BufferedWriter(new OutputStreamWriter(System.out), 512);
    }

    public Writer(OutputStream out) {
        this.out = new BufferedWriter(new OutputStreamWriter(out), 512);
    }

    void print(char c) throws IOException {
        out.write(c);
    }

    void print(String str) throws IOException {
        out.write(str);
    }

    void println() throws IOException {
        out.write("\n");
    }

    void flush() throws IOException {
        out.flush();
    }

    @Override
    protected void finalize() throws IOException {
        out.flush();
    }
}