Let a_1, …, a_n be an array of n positive integers. In one operation, you can choose an index i such that a_i = i, and remove a_i from the array (after the removal, the remaining parts are concatenated).

The weight of a is defined as the maximum number of elements you can remove.

You must answer q independent queries (x, y): after replacing the x first elements of a and the y last elements of a by n+1 (making them impossible to remove), what would be the weight of a?

Input

The first line contains two integers n and q (1 ≤ n, q ≤ 3 ⋅ 10^5) — the length of the array and the number of queries.

The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ n) — elements of the array.

The i-th of the next q lines contains two integers x and y (x, y ≥ 0 and x+y < n).

Output

Print q lines, i-th line should contain a single integer — the answer to the i-th query.

Examples

Input


13 5
2 2 3 9 5 4 6 5 7 8 3 11 13
3 1
0 0
2 4
5 0
0 12


Output


5
11
6
1
0


Input


5 2
1 4 1 2 4
0 0
1 0


Output


2
0

Note

Explanation of the first query:

After making first x = 3 and last y = 1 elements impossible to remove, a becomes [×, ×, ×, 9, 5, 4, 6, 5, 7, 8, 3, 11, ×] (we represent 14 as × for clarity).

Here is a strategy that removes 5 elements (the element removed is colored in red):

  * [×, ×, ×, 9, \color{red}{5}, 4, 6, 5, 7, 8, 3, 11, ×] 
  * [×, ×, ×, 9, 4, 6, 5, 7, 8, 3, \color{red}{11}, ×] 
  * [×, ×, ×, 9, 4, \color{red}{6}, 5, 7, 8, 3, ×] 
  * [×, ×, ×, 9, 4, 5, 7, \color{red}{8}, 3, ×] 
  * [×, ×, ×, 9, 4, 5, \color{red}{7}, 3, ×] 
  * [×, ×, ×, 9, 4, 5, 3, ×] (final state) 



It is impossible to remove more than 5 elements, hence the weight is 5.
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.util.Arrays;
import java.io.OutputStreamWriter;
import java.util.function.IntFunction;
import java.io.OutputStream;
import java.io.PrintStream;
import java.util.Iterator;
import java.io.IOException;
import java.io.UncheckedIOException;
import java.io.Closeable;
import java.io.Writer;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) throws Exception {
        Thread thread = new Thread(null, new TaskAdapter(), "", 1 << 29);
        thread.start();
        thread.join();
    }

    static class TaskAdapter implements Runnable {
        @Override
        public void run() {
            InputStream inputStream = System.in;
            OutputStream outputStream = System.out;
            FastInput in = new FastInput(inputStream);
            FastOutput out = new FastOutput(outputStream);
            CFixedPointRemoval solver = new CFixedPointRemoval();
            solver.solve(1, in, out);
            out.close();
        }
    }

    static class CFixedPointRemoval {
        Debug debug = new Debug(false);
        Segment seg;
        int n;
        IntegerBIT bit;

        public void solve(int testNumber, FastInput in, FastOutput out) {
            n = in.readInt();
            int q = in.readInt();
            int[] as = new int[n];
            int[] more = new int[n];
            int inf = (int) 1e8;
            for (int i = 0; i < n; i++) {
                as[i] = in.readInt() - 1;
                more[i] = i - as[i];
                if (more[i] < 0) {
                    more[i] = inf;
                }
            }

            Query[] qs = new Query[q];
            for (int i = 0; i < q; i++) {
                qs[i] = new Query();
                int x = in.readInt();
                int y = in.readInt();
                qs[i].l = x;
                qs[i].r = n - y - 1;
            }
            Query[] sorted = qs.clone();
            Arrays.sort(sorted, (a, b) -> Integer.compare(a.l, b.l));
            SimplifiedDeque<Query> dq = new Range2DequeAdapter<>(i -> sorted[i], 0, q - 1);
            bit = new IntegerBIT(n);
            seg = new Segment(0, n - 1);
            for (int i = n - 1; i >= 0; i--) {
                seg.updateSet(i, i, 0, n - 1, more[i]);
                update(0, 0, false);
                while (!dq.isEmpty() && dq.peekLast().l == i) {
                    Query query = dq.removeLast();
                    query.ans = bit.query(query.l + 1, query.r + 1);
                }
                debug.debug("bit", bit);
            }

            for (Query query : qs) {
                out.println(query.ans);
            }
        }

        public void update(int l, int r, boolean update) {
            if (update) {
                seg.update(l, r, 0, n - 1, -1);
            }
            while (true) {
                int first = seg.query(0, n - 1, 0, n - 1);
                if (first == -1) {
                    break;
                }
                bit.update(first + 1, 1);
                seg.updateSet(first, first, 0, n - 1, (int) 1e8);
                seg.update(first + 1, n - 1, 0, n - 1, -1);
            }
        }

    }

    static class IntegerBIT {
        private int[] data;
        private int n;

        public IntegerBIT(int n) {
            this.n = n;
            data = new int[n + 1];
        }

        public int query(int i) {
            int sum = 0;
            for (; i > 0; i -= i & -i) {
                sum += data[i];
            }
            return sum;
        }

        public int query(int l, int r) {
            return query(r) - query(l - 1);
        }

        public void update(int i, int mod) {
            if (i <= 0) {
                return;
            }
            for (; i <= n; i += i & -i) {
                data[i] += mod;
            }
        }

        public String toString() {
            StringBuilder builder = new StringBuilder();
            for (int i = 1; i <= n; i++) {
                builder.append(query(i) - query(i - 1)).append(' ');
            }
            return builder.toString();
        }

    }

    static interface SimplifiedStack<T> extends Iterable<T> {
        boolean isEmpty();

        T peekLast();

        T removeLast();

    }

    static class Segment implements Cloneable {
        private Segment left;
        private Segment right;
        private static int inf = (int) 1e8;
        private int min = inf;
        private int dirty;

        private void set(int x) {
            min = x;
        }

        private void modify(int x) {
            dirty += x;
            min += x;
        }

        public void pushUp() {
            min = Math.min(left.min, right.min);
        }

        public void pushDown() {
            if (dirty != 0) {
                left.modify(dirty);
                right.modify(dirty);
                dirty = 0;
            }
        }

        public Segment(int l, int r) {
            if (l < r) {
                int m = DigitUtils.floorAverage(l, r);
                left = new Segment(l, m);
                right = new Segment(m + 1, r);
                pushUp();
            } else {

            }
        }

        private boolean covered(int ll, int rr, int l, int r) {
            return ll <= l && rr >= r;
        }

        private boolean noIntersection(int ll, int rr, int l, int r) {
            return ll > r || rr < l;
        }

        public void updateSet(int ll, int rr, int l, int r, int x) {
            if (noIntersection(ll, rr, l, r)) {
                return;
            }
            if (covered(ll, rr, l, r)) {
                set(x);
                return;
            }
            pushDown();
            int m = DigitUtils.floorAverage(l, r);
            left.updateSet(ll, rr, l, m, x);
            right.updateSet(ll, rr, m + 1, r, x);
            pushUp();
        }

        public void update(int ll, int rr, int l, int r, int x) {
            if (noIntersection(ll, rr, l, r)) {
                return;
            }
            if (covered(ll, rr, l, r)) {
                modify(x);
                return;
            }
            pushDown();
            int m = DigitUtils.floorAverage(l, r);
            left.update(ll, rr, l, m, x);
            right.update(ll, rr, m + 1, r, x);
            pushUp();
        }

        public int query(int ll, int rr, int l, int r) {
            if (noIntersection(ll, rr, l, r) || min > 0) {
                return -1;
            }
            if (l == r) {
                return l;
            }
            pushDown();
            int m = DigitUtils.floorAverage(l, r);
            int ans = left.query(ll, rr, l, m);
            if (ans == -1) {
                ans = right.query(ll, rr, m + 1, r);
            }
            return ans;
        }

        private Segment deepClone() {
            Segment seg = clone();
            if (seg.left != null) {
                seg.left = seg.left.deepClone();
            }
            if (seg.right != null) {
                seg.right = seg.right.deepClone();
            }
            return seg;
        }

        protected Segment clone() {
            try {
                return (Segment) super.clone();
            } catch (CloneNotSupportedException e) {
                throw new RuntimeException(e);
            }
        }

        private void toString(StringBuilder builder) {
            if (left == null && right == null) {
                builder.append("val").append(",");
                return;
            }
            pushDown();
            left.toString(builder);
            right.toString(builder);
        }

        public String toString() {
            StringBuilder builder = new StringBuilder();
            deepClone().toString(builder);
            if (builder.length() > 0) {
                builder.setLength(builder.length() - 1);
            }
            return builder.toString();
        }

    }

    static class FastInput {
        private final InputStream is;
        private byte[] buf = new byte[1 << 13];
        private int bufLen;
        private int bufOffset;
        private int next;

        public FastInput(InputStream is) {
            this.is = is;
        }

        private int read() {
            while (bufLen == bufOffset) {
                bufOffset = 0;
                try {
                    bufLen = is.read(buf);
                } catch (IOException e) {
                    bufLen = -1;
                }
                if (bufLen == -1) {
                    return -1;
                }
            }
            return buf[bufOffset++];
        }

        public void skipBlank() {
            while (next >= 0 && next <= 32) {
                next = read();
            }
        }

        public int readInt() {
            int sign = 1;

            skipBlank();
            if (next == '+' || next == '-') {
                sign = next == '+' ? 1 : -1;
                next = read();
            }

            int val = 0;
            if (sign == 1) {
                while (next >= '0' && next <= '9') {
                    val = val * 10 + next - '0';
                    next = read();
                }
            } else {
                while (next >= '0' && next <= '9') {
                    val = val * 10 - next + '0';
                    next = read();
                }
            }

            return val;
        }

    }

    static class DigitUtils {
        private DigitUtils() {
        }

        public static int floorAverage(int x, int y) {
            return (x & y) + ((x ^ y) >> 1);
        }

    }

    static interface SimplifiedDeque<T> extends SimplifiedStack<T> {
    }

    static class Debug {
        private boolean offline;
        private PrintStream out = System.err;
        static int[] empty = new int[0];

        public Debug(boolean enable) {
            offline = enable && System.getSecurityManager() == null;
        }

        public Debug debug(String name, Object x) {
            return debug(name, x, empty);
        }

        public Debug debug(String name, Object x, int... indexes) {
            if (offline) {
                if (x == null || !x.getClass().isArray()) {
                    out.append(name);
                    for (int i : indexes) {
                        out.printf("[%d]", i);
                    }
                    out.append("=").append("" + x);
                    out.println();
                } else {
                    indexes = Arrays.copyOf(indexes, indexes.length + 1);
                    if (x instanceof byte[]) {
                        byte[] arr = (byte[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug(name, arr[i], indexes);
                        }
                    } else if (x instanceof short[]) {
                        short[] arr = (short[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug(name, arr[i], indexes);
                        }
                    } else if (x instanceof boolean[]) {
                        boolean[] arr = (boolean[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug(name, arr[i], indexes);
                        }
                    } else if (x instanceof char[]) {
                        char[] arr = (char[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug(name, arr[i], indexes);
                        }
                    } else if (x instanceof int[]) {
                        int[] arr = (int[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug(name, arr[i], indexes);
                        }
                    } else if (x instanceof float[]) {
                        float[] arr = (float[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug(name, arr[i], indexes);
                        }
                    } else if (x instanceof double[]) {
                        double[] arr = (double[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug(name, arr[i], indexes);
                        }
                    } else if (x instanceof long[]) {
                        long[] arr = (long[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug(name, arr[i], indexes);
                        }
                    } else {
                        Object[] arr = (Object[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug(name, arr[i], indexes);
                        }
                    }
                }
            }
            return this;
        }

    }

    static class FastOutput implements AutoCloseable, Closeable, Appendable {
        private StringBuilder cache = new StringBuilder(10 << 20);
        private final Writer os;

        public FastOutput append(CharSequence csq) {
            cache.append(csq);
            return this;
        }

        public FastOutput append(CharSequence csq, int start, int end) {
            cache.append(csq, start, end);
            return this;
        }

        public FastOutput(Writer os) {
            this.os = os;
        }

        public FastOutput(OutputStream os) {
            this(new OutputStreamWriter(os));
        }

        public FastOutput append(char c) {
            cache.append(c);
            return this;
        }

        public FastOutput append(int c) {
            cache.append(c);
            return this;
        }

        public FastOutput println(int c) {
            return append(c).println();
        }

        public FastOutput println() {
            cache.append(System.lineSeparator());
            return this;
        }

        public FastOutput flush() {
            try {
                os.append(cache);
                os.flush();
                cache.setLength(0);
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
            return this;
        }

        public void close() {
            flush();
            try {
                os.close();
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
        }

        public String toString() {
            return cache.toString();
        }

    }

    static class Query {
        int l;
        int r;
        int ans;

    }

    static class Range2DequeAdapter<T> implements SimplifiedDeque<T> {
        IntFunction<T> data;
        int l;
        int r;

        public Range2DequeAdapter(IntFunction<T> data, int l, int r) {
            this.data = data;
            this.l = l;
            this.r = r;
        }

        public boolean isEmpty() {
            return l > r;
        }

        public T peekLast() {
            return data.apply(r);
        }

        public T removeLast() {
            return data.apply(r--);
        }

        public Iterator<T> iterator() {
            return new Iterator<T>() {
                int iter = l;


                public boolean hasNext() {
                    return iter <= r;
                }


                public T next() {
                    return data.apply(iter++);
                }
            };
        }

    }
}

