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: Time Limit Exceeded)

H,W=map(int,input().split())

A=[]
B=[]
X=[]
for i in range(H):
    a,b=map(lambda x:int(x)-1,input().split())
    for j in range(a,b+1):
        X.append([i,j])
    
#dpの作成
dp=[[[float('inf')]*W for i in range(H+1)]for i in range(W)]
for i in range(W):
    for j in range(W):
        dp[i][0][j]=0

#ループ
for t in range(W):
    for s in range(t):
        dp[t][0][s]=float('inf')
    for i in range(1,H+1):
        for j in range(W):
            if j ==0:
                if [i-1,j] in X:
                    continue
                else:
                    dp[t][i][j]=dp[t][i-1][j]+1
            else:
                if [i-1,j] in X:
                    dp[t][i][j]=dp[t][i][j-1]+1
                else:
                    dp[t][i][j]=min(dp[t][i-1][j]+1,dp[t][i][j-1]+1)

#出力
for i in range(H):
    ans=float('inf')
    for t in range(W):
        for j in range(W):
            ans = min(ans,dp[t][i+1][j])
    if ans==float('inf'):
        print(-1)
    else:
        print(ans)