Problem: Snuke has a permutation (P_0,P_1,\cdots,P_{N-1}) of (0,1,\cdots,N-1).

Now, he will perform the following operation exactly once:

* Choose K consecutive elements in P and sort them in ascending order.



Find the number of permutations that can be produced as P after the operation.

Constraints

* 2 \leq N \leq 200000
* 2 \leq K \leq N
* 0 \leq P_i \leq N-1
* P_0,P_1,\cdots,P_{N-1} are all different.
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N K
P_0 P_1 \cdots P_{N-1}


Output

Print the number of permutations that can be produced as P after the operation.

Examples

Input

5 3
0 2 1 4 3


Output

2


Input

4 4
0 1 2 3


Output

1


Input

10 4
2 0 1 3 7 5 4 6 8 9


Output

6

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.FilterInputStream;
import java.io.BufferedInputStream;
import java.io.InputStream;

/**
 * @author khokharnikunj8
 */

public class Main {
    public static void main(String[] args) {
        new Thread(null, new Runnable() {
            public void run() {
                new Main().solve();
            }
        }, "1", 1 << 26).start();
    }

    void solve() {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        ScanReader in = new ScanReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        BSortingASegment solver = new BSortingASegment();
        solver.solve(1, in, out);
        out.close();
    }

    static class BSortingASegment {
        public void solve(int testNumber, ScanReader in, PrintWriter out) {
            int n = in.scanInt();
            int k = in.scanInt();
            int[] ar = new int[n];
            for (int i = 0; i < n; i++) {
                ar[i] = in.scanInt();
            }
            int[] minQ = new int[n + 5];
            int frontMin = 0;
            int backMin = 0;
            int[] maxQ = new int[n + 5];
            int frontMax = 0;
            int backMax = 0;
            int ans = 0;
            int[] maxx = new int[n];
            maxx[0] = 1;
            for (int i = 1; i < n; i++) {
                if (ar[i] > ar[i - 1]) maxx[i] = maxx[i - 1] + 1;
                else maxx[i] = 1;
            }
            for (int i = 0; i < k; i++) {
                while (frontMin < backMin && minQ[backMin - 1] > ar[i]) backMin--;
                minQ[backMin++] = ar[i];
                while (frontMax < backMax && maxQ[backMax - 1] < ar[i]) backMax--;
                maxQ[backMax++] = ar[i];
            }
            boolean done = false;
            if (maxx[k - 1] >= k) done = true;
            else ans++;
            for (int i = k; i < n; i++) {
                boolean flag = (frontMin < backMin && minQ[frontMin] == ar[i - k]);
                if (frontMin < backMin && minQ[frontMin] == ar[i - k]) frontMin++;
                if (frontMax < backMax && maxQ[frontMax] == ar[i - k]) frontMax++;
                while (frontMin < backMin && minQ[backMin - 1] > ar[i]) backMin--;
                minQ[backMin++] = ar[i];
                while (frontMax < backMax && maxQ[backMax - 1] < ar[i]) backMax--;
                maxQ[backMax++] = ar[i];
                flag &= (frontMax < backMax && ar[i] == maxQ[frontMax]);
                if (!flag) {
                    if (maxx[i] >= k) done = true;
                    else
                        ans++;
                }
            }
            if (done) ans++;

            out.println(ans);

        }

    }

    static class ScanReader {
        private byte[] buf = new byte[4 * 1024];
        private int index;
        private BufferedInputStream in;
        private int total;

        public ScanReader(InputStream inputStream) {
            in = new BufferedInputStream(inputStream);
        }

        private int scan() {
            if (index >= total) {
                index = 0;
                try {
                    total = in.read(buf);
                } catch (Exception e) {
                    e.printStackTrace();
                }
                if (total <= 0) return -1;
            }
            return buf[index++];
        }

        public int scanInt() {
            int integer = 0;
            int n = scan();
            while (isWhiteSpace(n)) n = scan();
            int neg = 1;
            if (n == '-') {
                neg = -1;
                n = scan();
            }
            while (!isWhiteSpace(n)) {
                if (n >= '0' && n <= '9') {
                    integer *= 10;
                    integer += n - '0';
                    n = scan();
                }
            }
            return neg * integer;
        }

        private boolean isWhiteSpace(int n) {
            if (n == ' ' || n == '\n' || n == '\r' || n == '\t' || n == -1) return true;
            else return false;
        }

    }
}