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.util.Arrays;
import java.util.Scanner;
import java.util.SortedMap;
import java.util.TreeMap;
import java.util.stream.IntStream;

/**
 * 解説通りに実装したソースコード
 * 
 * https://atcoder.jp/contests/abc177/submissions/16388865 にも参考
 */
public class Main {

	public static void main(String[] args) {
		try (Scanner scanner = new Scanner(System.in)) {
			int h = scanner.nextInt(), w = scanner.nextInt();
			int[] a = new int[h], b = new int[h];
			IntStream.range(0, h).forEach(i -> {
				a[i] = scanner.nextInt() - 1;
				b[i] = scanner.nextInt();
			});
			SortedMap<Integer, Integer> currToOrigin = new TreeMap<>();
			IntStream.range(0, w).forEach(j -> currToOrigin.put(j, j));
			int[] gaps = new int[w], results = new int[h];
			gaps[0] = w;
			Arrays.fill(results, -1);
			int minGapIndex = 0, maxGapIndex = 0;
			for (int i = 0; (i < h) && !currToOrigin.isEmpty(); i++) {
				SortedMap<Integer, Integer> subMap = currToOrigin.subMap(a[i], b[i]);
				if (!subMap.isEmpty()) {
					int maxOrigin = subMap.get(subMap.lastKey());
					subMap.forEach((key, value) -> gaps[key - value]--);
					subMap.clear();
					if ((b[i] < w) && !currToOrigin.containsKey(b[i])) {
						currToOrigin.put(b[i], maxOrigin);
						gaps[b[i] - maxOrigin]++;
						maxGapIndex = Math.max(maxGapIndex, b[i] - maxOrigin);
					}
					while ((minGapIndex <= maxGapIndex) && (0 == gaps[minGapIndex])) {
						minGapIndex++;
					}
				}
				results[i] = (minGapIndex <= maxGapIndex) ? minGapIndex + i + 1 : -1;
			}
			Arrays.stream(results).forEach(System.out::println);
		}
	}
}