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.sql.Array;
import java.util.*;
import java.io.*;


 public class TestClass {

    static class Parser
    {
        final private int BUFFER_SIZE = 1 << 16;

        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;

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

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

        //reads in the next string
        public String next() throws Exception
        {
            StringBuilder ret =  new StringBuilder();
            byte c = read();
            while (c <= ' ') c = read();
            do
            {
                ret = ret.append((char)c);
                c = read();
            } while (c > ' ');
            return ret.toString();
        }

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

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

        private byte read() throws Exception
        {
            if (bufferPointer == bytesRead) fillBuffer();
            return buffer[bufferPointer++];
        }
    }
    static class OutputWriter
    {
        private PrintWriter writer;

        public OutputWriter(OutputStream stream)
        {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(
                    stream)));
        }

        public OutputWriter(Writer writer)
        {
            this.writer = new PrintWriter(writer);
        }

        public void println(int x)
        {
            writer.println(x);
        }

        public void print(int x)
        {
            writer.print(x);
        }

        public void println(char x)
        {
            writer.println(x);
        }

        public void print(char x)
        {
            writer.print(x);
        }

        public void println(int array[], int size)
        {
            for (int i = 0; i < size; i++)
                println(array[i]);
        }

        public void print(int array[], int size)
        {
            for (int i = 0; i < size; i++)
                print(array[i] + " ");
        }

        public void println(long x)
        {
            writer.println(x);
        }

        public void print(long x)
        {
            writer.print(x);
        }

        public void println(long array[], int size)
        {
            for (int i = 0; i < size; i++)
                println(array[i]);
        }

        public void print(long array[], int size)
        {
            for (int i = 0; i < size; i++)
                print(array[i]);
        }

        public void println(float num)
        {
            writer.println(num);
        }

        public void print(float num)
        {
            writer.print(num);
        }

        public void println(double num)
        {
            writer.println(num);
        }

        public void print(double num)
        {
            writer.print(num);
        }

        public void println(String s)
        {
            writer.println(s);
        }

        public void print(String s)
        {
            writer.print(s);
        }

        public void println()
        {
            writer.println();
        }

        public void printSpace()
        {
            writer.print(" ");
        }

        public void printf(String format, Object args)
        {
            writer.printf(format, args);
        }

        public void flush()
        {
            writer.flush();
        }

        public void close()
        {
            writer.close();
        }
    }
    public static void main(String args[]) throws Exception {
        Parser s = new Parser(System.in);
        OutputWriter out = new OutputWriter(System.out);
       int N=s.nextInt();
        int a=s.nextInt();
        int b=s.nextInt();
        int turns=s.nextInt();
        long dp[][]=new long[2][N+1];

        for (int i = 1; i <=N ; i++) {
          if(i==b)
              continue;
            int dist=Math.abs(i-b)-1;
            int upper=Math.min(i+dist,N)-i;
            int lower=i-Math.max(i-dist,1);
            dp[0][i]=upper+lower;
        }
        long MOD=1000000007;
        if(turns==1){
            System.out.println(dp[0][a]%MOD);
            return;
        }
        for (int i = 1; i <= N; i++) {
            if (i == b) {
                continue;
            }
            dp[0][i] += dp[0][i - 1];
            dp[0][i]%=MOD;
        }

        for (int ks = 1; ks <turns ; ks++) {
            int curr=ks&1;
            int prev=(ks-1)&1;
            Arrays.fill(dp[curr],0);
            for (int i = 1; i <= N; i++) {
                if (i == b) {
                    continue;
                }
                int distance = Math.abs(b - i) - 1;
                int upper = Math.min(i + distance, N);
                int lower = Math.max(i - distance, 1);
                dp[curr][i] = (dp[prev][upper] - dp[prev][i] + MOD) % MOD;
                dp[curr][i] += (dp[prev][i - 1] - dp[prev][lower - 1] + MOD) % MOD;
            }
            for (int i = 1; i <= N; i++) {
                dp[curr][i] = (dp[curr][i] + dp[curr][i - 1]) % MOD;
            }
        }
        long res = (dp[(turns - 1) & 1][a] - dp[(turns - 1) & 1][a - 1] + MOD) % MOD;
        System.out.println(res);





    }}