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.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.lang.reflect.Field;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collection;
import java.util.EnumSet;
import java.util.NoSuchElementException;
import java.util.function.IntBinaryOperator;
import java.util.function.IntUnaryOperator;
import java.util.function.LongUnaryOperator;


public class Main {
    public static void main(String[] args) throws Exception {
        Field f = System.out.getClass().getDeclaredField("autoFlush");
        f.setAccessible(true);
        f.set(System.out, false);
        execute(System.in, System.out);
    }

    public static void execute(InputStream in, OutputStream out) {
        ExtendedScanner s = new ExtendedScanner(in);
        Out o = new Out(out);
        solve(s, o);
        o.flush();
        o.close();
    }

    public static void solve(ExtendedScanner sc, Out out) {
        int n = sc.nextInt();
        int k = sc.nextInt();
        int[] p = sc.ints(n);
        IntSparseTable min = new IntSparseTable(p, new IntBoundedSemiLattice(Integer::min, n));
        IntSparseTable max = new IntSparseTable(p, new IntBoundedSemiLattice(Integer::max, 0));
        int[] a = new int[n];
        a[n - 1] = 1;
        for (int i = n - 2; i >= 0; i--) {
            a[i] = p[i] < p[i + 1] ? a[i + 1] + 1 : 1;
        }
        boolean[] b = new boolean[n];
        for (int i = n - 2; i >= 0; i--) {
            b[i] = b[i + 1] || a[i + 1] >= k;
        }
        int c = n - k + 1;
        for (int i = 0; i < n - k; i++) {
            if (a[i] >= k) {
                if (b[i]) c--;
            } else {
                int x = min.query(i + 1, i + k);
                int y = max.query(i + 1, i + k);
                if (p[i] < x && y < p[i + k]) {
                    c--;
                }
            }
        }
        out.writeln(c);
    }
}


/**
 * @author https://atcoder.jp/users/suisen
 */
class BasicScanner {
    private final InputStream in;
    private final byte[] buf = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;
    public BasicScanner(InputStream in) {this.in = in;}
    private boolean hasNextByte() {
        if (ptr < buflen) return true;
        ptr = 0;
        try {buflen = in.read(buf);}
        catch (final IOException e) {e.printStackTrace();}
        return buflen > 0;
    }
    private int readByte() {return hasNextByte() ? buf[ptr++] : -1;}
    public boolean hasNext() {
        while (hasNextByte() && !(33 <= buf[ptr] && buf[ptr] <= 126)) ptr++;
        return hasNextByte();
    }
    private StringBuilder nextSequence() {
        if (!hasNext()) throw new NoSuchElementException();
        final StringBuilder sb = new StringBuilder();
        int b = readByte();
        while (33 <= b && b <= 126) {sb.appendCodePoint(b); b = readByte();}
        return sb;
    }
    public char nextChar() {
        return (char) readByte();
    }
    public String next() {
        return nextSequence().toString();
    }
    public String next(int len) {
        return new String(nextChars(len));
    }
    public char[] nextChars() {
        final StringBuilder sb = nextSequence();
        int l = sb.length();
        char[] dst = new char[l];
        sb.getChars(0, l, dst, 0);
        return dst;
    }
    public char[] nextChars(int len) {
        if (!hasNext()) throw new NoSuchElementException();
        char[] s = new char[len];
        int i = 0;
        int b = readByte();
        while (33 <= b && b <= 126 && i < len) {s[i++] = (char) b; b = readByte();}
        if (i != len) throw new NoSuchElementException(String.format("length %d is longer than the sequence.", len));
        return s;
    }
    public long nextLong() {
        if (!hasNext()) throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {minus = true; b = readByte();}
        if (b < '0' || '9' < b) throw new NumberFormatException();
        while (true) {
            if ('0' <= b && b <= '9') n = n * 10 + b - '0';
            else if (b == -1 || !(33 <= b && b <= 126)) return minus ? -n : n;
            else throw new NumberFormatException();
            b = readByte();
        }
    }
    public int nextInt() {return Math.toIntExact(nextLong());}
    public double nextDouble() {return Double.parseDouble(next());}
}



abstract class IntMagma extends PropertyHolder {
    protected final IntBinaryOperator operator;
    public IntMagma(final IntBinaryOperator operator, final EnumSet<Property> properties) {
        super(properties);
        this.operator = operator;
    }
    public IntMagma(final IntBinaryOperator operator, final TypicalPropertySets properties) {
        super(properties);
        this.operator = operator;
    }
    public final int apply(final int left, final int right) {return operator.applyAsInt(left, right);}
}


/**
 * @author https://atcoder.jp/users/suisen
 */
class Out {
    private final OutputStream out;
    private byte[] buf = new byte[1024];
    private int ptr = 0;
    private static final int AUTO_FLUSH_THRETHOLD = 1 << 17;

    public Out(OutputStream out) {
        this.out = out;
    }

    public void flush() {
        try {
            out.write(buf, 0, ptr);
            out.flush();
            ptr = 0;
        } catch (IOException e) {e.printStackTrace();}
    }

    public void close() {
        try {out.close();} catch (IOException e) {e.printStackTrace();}
    }

    public Out writeln() {return write('\n');}
    public Out writeln(Object o) {return write(o).write('\n');}
    public Out writeln(String s) {return write(s).write('\n');}
    public Out writeln(char[] c) {return write(c).write('\n');}
    public Out writeln(char   c) {return write(c).write('\n');}
    public Out writeln(byte   b) {return write(b).write('\n');}
    public Out writeln(int    x) {return write(x).write('\n');}
    public Out writeln(long   x) {return write(x).write('\n');}
    public Out writeln(double d) {return write(d).write('\n');}

    public Out writeSpace() {return write(' ');}
    
    public Out write(Object o) {
        return write(o.toString());
    }

    public Out write(String s) {
        try {
            Field strValueField = s.getClass().getDeclaredField("value");
            strValueField.setAccessible(true);
            byte[] b = (byte[]) strValueField.get(s);
            int l = s.length();
            if (l > AUTO_FLUSH_THRETHOLD) {
                flush();
                int i = 0;
                while (i + AUTO_FLUSH_THRETHOLD < l) {
                    out.write(b, i, AUTO_FLUSH_THRETHOLD);
                    out.flush();
                    i += AUTO_FLUSH_THRETHOLD;
                }
                ensureCapacity(l - i);
                System.arraycopy(b, i, buf, 0, l - i);
                ptr = l - i;
            } else {
                ensureCapacity(ptr + l);
                System.arraycopy(b, 0, buf, ptr, l);
                ptr += l;
            }
        } catch (Exception e) {e.printStackTrace();}
        return this;
    }

    public Out write(char[] c) {
        int l = c.length;
        if (l > AUTO_FLUSH_THRETHOLD) {
            flush();
            ensureCapacity(AUTO_FLUSH_THRETHOLD);
            int i = 0;
            while (i + AUTO_FLUSH_THRETHOLD < l) {
                for (int j = 0; j < AUTO_FLUSH_THRETHOLD; j++) {
                    buf[ptr++] = (byte) c[i + j];
                }
                flush();
                i += AUTO_FLUSH_THRETHOLD;
            }
            for (; i < l; i++) {
                buf[ptr++] = (byte) c[i];
            }
        } else {
            ensureCapacity(ptr + l);
            for (char ch : c) buf[ptr++] = (byte) ch;
        }
        return this;
    }

    public Out write(char c) {
        ensureCapacity(ptr + 1);
        buf[ptr++] = (byte) c;
        return this;
    }

    public Out write(byte b) {
        ensureCapacity(ptr + 1);
        buf[ptr++] = b;
        return this;
    }

    public Out write(int x) {
        if (x == 0) {
            ensureCapacity(ptr + 1);
            buf[ptr++] = '0';
            return this;
        }
        int d = stringSize(x);
        ensureCapacity(ptr + d);
        if (x < 0) {
            buf[ptr++] = '-';
            x = -x;
            d--;
        }
        int j = ptr + d; 
        while (x > 0) {
            buf[--j] = (byte) ('0' + (x % 10));
            x /= 10;
        }
        ptr += d;
        return this;
    }

    public Out write(long x) {
        if (x == 0) {
            ensureCapacity(ptr + 1);
            buf[ptr++] = '0';
            return this;
        }
        int d = stringSize(x);
        ensureCapacity(ptr + d);
        if (x < 0) {
            buf[ptr++] = '-';
            x = -x;
            d--;
        }
        int j = ptr + d; 
        while (x > 0) {
            buf[--j] = (byte) ('0' + (x % 10));
            x /= 10;
        }
        ptr += d;
        return this;
    }

    public Out write(double d) {
        return write(Double.toString(d));
    }

    private void ensureCapacity(int cap) {
        if (cap > AUTO_FLUSH_THRETHOLD) {
            flush();
        }
        if (cap >= buf.length) {
            int newLength = buf.length;
            while (newLength < cap) newLength <<= 1;
            byte[] newBuf = new byte[newLength];
            System.arraycopy(buf, 0, newBuf, 0, buf.length);
            buf = newBuf;
        }
    }
    private static int stringSize(long x) {
        int d = 1;
        if (x >= 0) {d = 0; x = -x;}
        long p = -10;
        for (int i = 1; i < 19; i++, p *= 10) if (x > p) return i + d;
        return 19 + d;
    }
    private static int stringSize(int x) {
        int d = 1;
        if (x >= 0) {d = 0; x = -x;}
        int p = -10;
        for (int i = 1; i < 10; i++, p *= 10) if (x > p) return i + d;
        return 10 + d;
    }
}


/**
 * @author https://atcoder.jp/users/suisen
 * 
 * for Static Range Query. (Monoid)
 * build: O(N*logN). query: O(1).
 */
final class IntSparseTable {
    private final int n;
    private final int[][] table;
    private final IntBoundedSemiLattice bsl;
    private final int[] flExp;
    
    /**
     * CAUTION: bounded-semilattice meats idempotent law and bond law. bsl is in monoid. (max, min, gcd, lcm, and, or, ...)
     * So, there exists some monoid s.t. Sparse Table cannot handle. (ex. addition, xor, multiplication)
     * @param a int array.
     * @param bsl (max, min, gcd, lcm, and, or, rewrite, ...) NOT (addition, xor, multiplication, ...)
     */
    public IntSparseTable(final int[] a, final IntBoundedSemiLattice bsl) {
        this.n = a.length;
        this.table = new int[n][];
        this.bsl = bsl;
        this.flExp = new int[n + 1];
        for (int i = 1; i <= n; i++) this.flExp[i] = Integer.SIZE - Integer.numberOfLeadingZeros(i) - 1;
        buildTable(a);
    }

    public int query(final int i, final int j) {
        if (j <= i) return bsl.e;
        final int exp = flExp[j - i];
        return bsl.apply(table[i][exp], table[j - (1 << exp)][exp]);
    }

    private void buildTable(final int[] a) {
        for (int i = 0; i < n; i++) {
            table[i] = new int[flExp[n - i] + 1];
            table[i][0] = a[i];
        }
        for (int i = n - 1; i >= 0; i--) {
            final int[] e = table[i];
            for (int j = 1, k = 1; j < e.length; j++, k <<= 1) {
                e[j] = bsl.apply(e[j - 1], table[i + k][j - 1]);
            }
        }
    }
}



class IntMonoid extends IntMagma implements IntUnital {
    public final int e;
    public IntMonoid(final IntBinaryOperator operator, final int e) {
        super(operator, TypicalPropertySets.MONOID);
        this.e = e;
    }
    @Override
    public int identityElement() {return e;}
    public static <M extends IntMagma & IntUnital> IntMonoid of(M m) {
        m.requireProperties(TypicalPropertySets.MONOID);
        return new IntMonoid(m.operator, m.identityElement());
    }
}


/**
 * @author https://atcoder.jp/users/suisen
 */
final class ExtendedScanner extends BasicScanner {
    public ExtendedScanner(InputStream in) {super(in);}
    public int[] ints(final int n) {
        final int[] a = new int[n];
        Arrays.setAll(a, $ -> nextInt());
        return a;
    }
    public int[] ints(final int n, final IntUnaryOperator f) {
        final int[] a = new int[n];
        Arrays.setAll(a, $ -> f.applyAsInt(nextInt()));
        return a;
    }
    public int[][] ints(final int n, final int m) {
        final int[][] a = new int[n][];
        Arrays.setAll(a, $ -> ints(m));
        return a;
    }
    public int[][] ints(final int n, final int m, final IntUnaryOperator f) {
        final int[][] a = new int[n][];
        Arrays.setAll(a, $ -> ints(m, f));
        return a;
    }
    public long[] longs(final int n) {
        final long[] a = new long[n];
        Arrays.setAll(a, $ -> nextLong());
        return a;
    }
    public long[] longs(final int n, final LongUnaryOperator f) {
        final long[] a = new long[n];
        Arrays.setAll(a, $ -> f.applyAsLong(nextLong()));
        return a;
    }
    public long[][] longs(final int n, final int m) {
        final long[][] a = new long[n][];
        Arrays.setAll(a, $ -> longs(m));
        return a;
    }
    public long[][] longs(final int n, final int m, final LongUnaryOperator f) {
        final long[][] a = new long[n][];
        Arrays.setAll(a, $ -> longs(m, f));
        return a;
    }
    public char[][] charArrays(final int n) {
        final char[][] c = new char[n][];
        Arrays.setAll(c, $ -> nextChars());
        return c;
    }
    public char[][] charArrays(final int n, final int m) {
        final char[][] c = new char[n][];
        Arrays.setAll(c, $ -> nextChars(m));
        return c;
    }
    public double[] doubles(final int n) {
        final double[] a = new double[n];
        Arrays.setAll(a, $ -> nextDouble());
        return a;
    }
    public double[][] doubles(final int n, final int m) {
        final double[][] a = new double[n][];
        Arrays.setAll(a, $ -> doubles(m));
        return a;
    }
    public String[] strings(final int n) {
        final String[] s = new String[n];
        Arrays.setAll(s, $ -> next());
        return s;
    }
    public String[] strings(final int n, final int m) {
        final String[] s = new String[n];
        Arrays.setAll(s, $ -> next(m));
        return s;
    }
}



class IntBoundedSemiLattice extends IntMonoid {
    public IntBoundedSemiLattice(final IntBinaryOperator operator, final int e) {
        super(operator, e);
        addProperties(Property.IDEMPOTENT, Property.COMMUTATIVE);
    }
    public static <M extends IntMagma & IntUnital> IntBoundedSemiLattice of(M m) {
        m.requireProperties(TypicalPropertySets.BOUNDED_SEMI_LATTICE.getProperties());
        return new IntBoundedSemiLattice(m.operator, m.identityElement());
    }
}

enum Property {ANNIHILATED_BY_ZERO, ASSOCIATIVE, CANCELLATIVE, COMMUTATIVE, DISTRIBUTIVE, IDEMPOTENT;}


enum TypicalPropertySets {
    ABELIAN_GROUP(EnumSet.of(Property.ASSOCIATIVE, Property.CANCELLATIVE, Property.COMMUTATIVE)),
    BOUNDED_SEMI_LATTICE(EnumSet.of(Property.ASSOCIATIVE, Property.COMMUTATIVE, Property.IDEMPOTENT)),
    COMMUTATIVE_MONOID(EnumSet.of(Property.ASSOCIATIVE, Property.COMMUTATIVE)),
    GROUP(EnumSet.of(Property.ASSOCIATIVE, Property.CANCELLATIVE)),
    MONOID(EnumSet.of(Property.ASSOCIATIVE)),
    SEMI_GROUP(EnumSet.of(Property.ASSOCIATIVE)),
    SEMI_LATTICE(EnumSet.of(Property.ASSOCIATIVE, Property.IDEMPOTENT, Property.COMMUTATIVE)),
    SEMI_RING(EnumSet.of(Property.DISTRIBUTIVE, Property.ANNIHILATED_BY_ZERO)),
    RING(EnumSet.of(Property.DISTRIBUTIVE, Property.ANNIHILATED_BY_ZERO));
    private final EnumSet<Property> properties;
    private TypicalPropertySets(EnumSet<Property> properties) {this.properties = properties;}
    public final EnumSet<Property> getProperties() {return properties.clone();}
}

interface IntUnital {int identityElement();}


abstract class PropertyHolder {
    private final EnumSet<Property> properties;
    public PropertyHolder(final EnumSet<Property> properties) {this.properties = properties;}
    public PropertyHolder(final TypicalPropertySets typicalSet) {this(typicalSet.getProperties());}
    public final EnumSet<Property> getProperties() {return properties;}
    public final void addProperties(final Property... props) {for (Property prop : props) properties.add(prop);}
    public final void addProperties(final EnumSet<Property> props) {for (Property prop : props) properties.add(prop);}
    public final void addProperties(final TypicalPropertySets props) {addProperties(props.getProperties());}
    public final boolean hasProperties(final Property... props) {
        for (final Property prop : props) if (!properties.contains(prop)) return false;
        return true;
    }
    public final boolean hasProperties(final EnumSet<Property> props) {
        for (final Property prop : props) if (!properties.contains(prop)) return false;
        return true;
    }
    public final boolean hasProperties(final TypicalPropertySets props) {return hasProperties(props.getProperties());}
    public final void requireProperties(final EnumSet<Property> props, final Property... ps) {
        final ArrayList<Property> unmet = new ArrayList<>();
        for (final Property prop : props) if (!properties.contains(prop)) unmet.add(prop);
        for (final Property prop : ps) if (!properties.contains(prop)) unmet.add(prop);
        if (unmet.size() > 0) throw new UnsatisfiedRequiredPropertiesException(unmet);
    }
    public final void requireProperties(final TypicalPropertySets props, final Property... ps) {
        requireProperties(props.getProperties(), ps);
    }
    private static final class UnsatisfiedRequiredPropertiesException extends RuntimeException {
        private static final long serialVersionUID = 1L;
        private UnsatisfiedRequiredPropertiesException(final Collection<Property> props) {
            for (final Property prop : props) System.err.println(prop.name() + "should be satisfied.");
        }
    }
}