Problem:
Score : 600 points

Problem Statement

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.

Sample Input 1

4 4
2 4
1 1
2 3
2 4

Sample Output 1

1
3
6
-1

Let (i,j) denote the square at the i-th row from the top and j-th column from the left.

For k=1, we need one move such as (1,1) → (2,1).

For k=2, we need three moves such as (1,1) → (2,1) → (2,2) → (3,2).

For k=3, we need six moves such as (1,1) → (2,1) → (2,2) → (3,2) → (3,3) → (3,4) → (4,4).

For k=4, it is impossible to reach any square in the fifth row from the top.

Solution in Java (OpenJDK 11.0.6) (judge verdict: Runtime Error)


import java.util.Scanner;

/**
 * Created by enpingkuang on 2020/9/12 6:54 下午
 */
public class Main {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int h = scanner.nextInt();
        int w = scanner.nextInt();
        int[][] ans = new int[w+1][h+1];
        int[] l = new int[w+1];
        int[] r = new int[w+1];
        for(int i = 1;i<=h;i++){
            l[i] = scanner.nextInt();
            r[i] = scanner.nextInt();
        }
        for(int j = 1;j<=w;j++) {
            int right = j;
            for (int i = 1; i <= h; i++) {
                if (ans[j][i-1] == -1) {
                    ans[j][i] = -1;
                    continue;
                }
                if (right < l[i]) {
                    ans[j][i] = ans[j][i-1] + 1;
                } else {
                    int tmp = Math.max(r[i] + 1, right);
                    if (tmp <= w) {
                        ans[j][i] = ans[j][i-1] + 1 + tmp - right;
                        right = tmp;
                    } else {
                        ans[j][i] = -1;
                    }
                }
            }
        }
        for(int i = 1;i<=h;i++){
            int min = -1;
            for(int j=1;j<=w;j++){
                if(ans[j][i] != -1) {
                    if(min != -1) {
                        min = Math.min(ans[j][i], min);
                    }else{
                        min = ans[j][i];
                    }
                }
            }
            System.out.println(min);
        }
    }
}