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: Time Limit Exceeded)

#include <bits/stdc++.h>
using namespace std;
typedef long long LL;
const int N = 2e5 + 10, INF = 0x3f3f3f3f;
int n, m, s, t, ans, i, j, a[N];
int main() {
	cin >> n >> m >> s >> t;
	a[0] = INF;
	for (i = 2; i <= n + 1; i++) {
		for (j = 1; j <= m; j++) {
			if (j >= s && j <= t) a[j] = a[j - 1] + 1;
			else a[j] = min(a[j], a[j - 1]) + 1;
		}
		for (j = 1, ans = INF; j <= m; j++) ans = min(ans, a[j]);
		cout << (ans == INF ? -1 : ans) << '\n';
		if (i <= n) cin >> s >> t;
	}
	return 0; 
}