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 C (GCC 9.2.1) (judge verdict: Runtime Error)

#include<stdio.h>
int qx[1000000],qy[1000000],count[1000000],record[1000000],l[1000000],r[1000000];
int main(){
	int h,w;
	scanf("%d %d",&h,&w);
	for (int i=2;i<=h+1;i++)
	  record[i]=1000000;
	for (int i=1;i<=h;i++){
		scanf("%d %d",&l[i],&r[i]);
	}
	qx[1]=1;
	qy[1]=1;
	count[1]=0;
	int head=0;
	int tail=1;
	while (head<tail){
		head++;
		int x=qx[head];
		int y=qy[head];
		if (y<l[x]||y>r[x]){
			tail++;
			qx[tail]=x+1;
			qy[tail]=y;
			count[tail]=count[head]+1;
			if (record[x+1]>count[tail])
			  record[x+1]=count[tail];
		}
		if (y!=w){
			tail++;
			qx[tail]=x;
			qy[tail]=y+1;
			count[tail]=count[head]+1;	
		}
	}
	for (int i=2;i<=h+1;i++){
		if (record[i]==1000000){
			printf("-1\n");
		}else printf("%d\n",record[i]);
	}
}