Problem: There is a grid of squares with H+1 horizontal rows and W vertical columns.

You will start at one of the squares in the top row and repeat moving one square right or down. However, for each integer i from 1 through H, you cannot move down from the A_i-th, (A_i + 1)-th, \ldots, B_i-th squares from the left in the i-th row from the top.

For each integer k from 1 through H, find the minimum number of moves needed to reach one of the squares in the (k+1)-th row from the top. (The starting square can be chosen individually for each case.) If, starting from any square in the top row, none of the squares in the (k+1)-th row can be reached, print `-1` instead.

Constraints

* 1 \leq H,W \leq 2\times 10^5
* 1 \leq A_i \leq B_i \leq W

Input

Input is given from Standard Input in the following format:


H W
A_1 B_1
A_2 B_2
:
A_H B_H


Output

Print H lines. The i-th line should contain the answer for the case k=i.

Example

Input

4 4
2 4
1 1
2 3
2 4


Output

1
3
6
-1

Solution (in JAVA):

Solution:
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Comparator;
import java.util.HashMap;
import java.util.InputMismatchException;
import java.util.Iterator;
import java.util.List;
import java.util.Map;
import java.util.NavigableMap;
import java.util.NoSuchElementException;
import java.util.Objects;
import java.util.Optional;
import java.util.OptionalInt;
import java.util.Set;
import java.util.TreeMap;

public class Main {
    void solve(MyScanner in, MyWriter out) {
        int h = in.nextInt();
        int w = in.nextInt();
        var map = new TreeMap<Integer, Integer>();
        for (int i = 0; i < w; i++) {
            map.put(i, i);
        }
        var mset = new SortedMultiset<Integer>();
        mset.add(0, w);
        for (int i = 1; i <= h; i++) {
            int a = in.nextInt() - 1;
            int b = in.nextInt();
            var sub = map.subMap(a, true, b, true);
            for (Map.Entry<Integer, Integer> e : sub.entrySet()) {
                int to = e.getKey();
                int from = e.getValue();
                mset.remove(to - from);
            }
            OptionalInt rightest = sub.values().stream().mapToInt(e -> e).max();
            sub.clear();
            if (rightest.isPresent() && b < w) {
                map.put(b, rightest.getAsInt());
                mset.add(b - rightest.getAsInt());
            }
            final int j = i;
            mset.first().ifPresentOrElse(ans -> {
                out.println(j + ans);
            }, () -> {
                out.println(-1);
            });
        }
    }
    static final class SortedMultiset<E> extends Multiset<E> {
        final NavigableMap<E, Long> navMap;
        SortedMultiset() {
            this(new TreeMap<>());
        }
        SortedMultiset(Comparator<? super E> c) {
            this(new TreeMap<>(c));
        }
        private SortedMultiset(NavigableMap<E, Long> navMap) {
            super(navMap);
            this.navMap = navMap;
        }
        Optional<E> first() {
            return navMap.isEmpty()
                    ? Optional.empty()
                    : Optional.of(navMap.firstKey());
        }
        Optional<E> last() {
            return navMap.isEmpty()
                    ? Optional.empty()
                    : Optional.of(navMap.lastKey());
        }
        Optional<E> pollFirst() {
            Optional<E> o = first();
            if (o.isPresent())
                remove(o.get());
            return o;
        }
        Optional<E> pollLast() {
            Optional<E> o = last();
            if (o.isPresent())
                remove(o.get());
            return o;
        }
    }
    static class Multiset<E> {
        final Map<E, Long> map;
        Multiset() {
            this(new HashMap<>());
        }
        Multiset(Map<E, Long> map) {
            this.map = map;
        }
        boolean add(E e) {
            add(e, 1);
            return true;
        }
        boolean add(E e, long count) {
            Objects.requireNonNull(e);
            if (count < 0)
                throw new IllegalArgumentException();
            if (count > 0) {
                map.merge(e, count, Math::addExact);
                return true;
            }
            return false;
        }
        boolean remove(E e) {
            return remove(e, 1);
        }
        boolean remove(E e, long count) {
            if (count < 0)
                throw new IllegalArgumentException();
            if (count == 0)
                return false;
            Long oldValue = map.get(e);
            if (oldValue == null)
                return false;
            long newValue = oldValue - count;
            if (newValue <= 0)
                map.remove(e);
            else
                map.put(e, newValue);
            return true;
        }
        boolean removeAll(E e) {
            return remove(e, Long.MAX_VALUE);
        }
        long count(E e) {
            return map.getOrDefault(e, 0L);
        }
        boolean contains(E e) {
            return map.containsKey(e);
        }
        boolean isEmpty() {
            return map.isEmpty();
        }
        Set<E> elementSet() {
            return map.keySet();
        }
    }
    public static void main(String[] args) {
        MyWriter w = new MyWriter(System.out);
        new Main().solve(new MyScanner(System.in), w);
        w.flush();
    }
    static final class MyScanner {
        static final int BUFFER_SIZE = 8192;
        private final InputStream in;
        private final byte[] buffer = new byte[BUFFER_SIZE];
        private int point;
        private int readLength;

        MyScanner(InputStream in) {
            this.in = in;
        }
        private int readByte() {
            if (point < readLength) {
                int result = buffer[point];
                point += 1;
                return result;
            }
            try {
                readLength = in.read(buffer);
            } catch (IOException e) {
                throw new AssertionError(null, e);
            }
            if (readLength == -1) {
                return -1;
            }
            point = 1;
            return buffer[0];
        }
        private static boolean isVisibleChar(int c) {
            return 33 <= c && c <= 126;
        }
        char nextChar() {
            int c = readByte();
            while (!(c == -1 || isVisibleChar(c))) {
                c = readByte();
            }
            if (c == -1) {
                throw new NoSuchElementException();
            }
            return (char)c;
        }
        String next() {
            return next(16);
        }
        String next(int n) {
            int c = readByte();
            while (!(c == -1 || isVisibleChar(c))) {
                c = readByte();
            }
            if (c == -1) {
                throw new NoSuchElementException();
            }
            StringBuilder b = new StringBuilder(n);
            do {
                b.append((char)c);
                c = readByte();
            } while (c != -1 && isVisibleChar(c));
            return b.toString();
        }
        long nextLong() {
            int c = readByte();
            while (!(c == -1 || isVisibleChar(c))) {
                c = readByte();
            }
            if (c == -1) {
                throw new NoSuchElementException();
            }
            boolean minus = false;
            long limit = -Long.MAX_VALUE;
            if (c == '-') {
                minus = true;
                limit = Long.MIN_VALUE;
                c = readByte();
            }
            long n = 0L;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                if (n < limit / 10L) {
                    throw new InputMismatchException();
                }
                n *= 10L;
                int digit = c - '0';
                if (n < limit + digit) {
                    throw new InputMismatchException();
                }
                n -= digit;
                c = readByte();
            } while (c != -1 && isVisibleChar(c));
            return minus ? n : -n;
        }
        int nextInt() {
            long n = nextLong();
            if (n < Integer.MIN_VALUE || n > Integer.MAX_VALUE) {
                throw new InputMismatchException();
            }
            return (int)n;
        }
        double nextDouble() {
            return Double.parseDouble(next());
        }
        int[] nextIntArray(int n) {
            int[] result = new int[n];
            for (int i = 0; i < n; i++) {
                result[i] = nextInt();
            }
            return result;
        }
        long[] nextLongArray(int n) {
            long[] result = new long[n];
            for (int i = 0; i < n; i++) {
                result[i] = nextLong();
            }
            return result;
        }
        char[] nextCharArray(int n) {
            char[] result = new char[n];
            for (int i = 0; i < n; i++) {
                result[i] = nextChar();
            }
            return result;
        }
        char[][] next2dCharArray(int h, int w) {
            char[][] result = new char[h][w];
            for (int i = 0; i < h; i++) {
                for (int j = 0; j < w; j++) {
                    result[i][j] = nextChar();
                }
            }
            return result;
        }
        int[][] nextVerticalIntArrays(int arrayCount, int arrayLength) {
            int[][] result = new int[arrayCount][arrayLength];
            for (int i = 0; i < arrayLength; i++) {
                for (int j = 0; j < arrayCount; j++) {
                    result[j][i] = nextInt();
                }
            }
            return result;
        }
        long[][] nextVerticalLongArrays(int arrayCount, int arrayLength) {
            long[][] result = new long[arrayCount][arrayLength];
            for (int i = 0; i < arrayLength; i++) {
                for (int j = 0; j < arrayCount; j++) {
                    result[j][i] = nextLong();
                }
            }
            return result;
        }
        char[][] nextVerticalCharArrays(int arrayCount, int arrayLength) {
            char[][] result = new char[arrayCount][arrayLength];
            for (int i = 0; i < arrayLength; i++) {
                for (int j = 0; j < arrayCount; j++) {
                    result[j][i] = nextChar();
                }
            }
            return result;
        }
        List<String> nextStringList(int n) {
            var result = new ArrayList<String>(n);
            for (int i = 0; i < n; i++) {
                result.add(next());
            }
            return result;
        }
        List<Integer> nextIntList(int n) {
            var result = new ArrayList<Integer>(n);
            for (int i = 0; i < n; i++) {
                result.add(nextInt());
            }
            return result;
        }
        List<Long> nextLongList(int n) {
            var result = new ArrayList<Long>(n);
            for (int i = 0; i < n; i++) {
                result.add(nextLong());
            }
            return result;
        }
    }
    static final class MyWriter extends PrintWriter {
        MyWriter(OutputStream out) {
            super(out);
        }
        void println(int[] x) {
            println(x, " ");
        }
        void println(int[] x, String delimiter) {
            if (x.length > 0) {
                print(x[0]);
                for (int i = 1; i < x.length; i++) {
                    print(delimiter);
                    print(x[i]);
                }
            }
            println();
        }
        void println(long[] x) {
            println(x, " ");
        }
        void println(long[] x, String delimiter) {
            if (x.length > 0) {
                print(x[0]);
                for (int i = 1; i < x.length; i++) {
                    print(delimiter);
                    print(x[i]);
                }
            }
            println();
        }
        void println(Iterable<?> iterable) {
            println(iterable, " ");
        }
        void println(Iterable<?> iterable, String delimiter) {
            Iterator<?> i = iterable.iterator();
            if (i.hasNext()) {
                print(i.next());
                while (i.hasNext()) {
                    print(delimiter);
                    print(i.next());
                }
            }
            println();
        }
        void printLines(int[] x) {
            println(x, System.lineSeparator());
        }
        void printLines(long[] x) {
            println(x, System.lineSeparator());
        }
        void printLines(Iterable<?> iterable) {
            println(iterable, System.lineSeparator());
        }
    }
}