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 PyPy3 (7.3.0) (judge verdict: Wrong Answer)

import sys
input = sys.stdin.buffer.readline

h,w = map(int,input().split())

x = 1
A = []
B = []
kouho = [1]
for i in range(h):
    AA,BB = map(int,input().split())
    A.append(AA)
    B.append(BB)
    if i<=200 == 0:
        if AA != 1:
            kouho.append(AA-1)
        if BB != w:
            kouho.append(BB+1)


dp = [10**6] * h
for start in kouho:
    x = start
    for i in range(h):
        a,b = A[i],B[i]
        if a <= x <= b:
            x = b+1
        if x != w+1:
            dp[i] = min(dp[i],x+i)

for i in range(h):
    if dp[i] == 10**6:
        print(-1)
    else:
        print(dp[i])