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: Wrong Answer)

/*{{{*/
#include<bits/stdc++.h>

typedef long long ll;

#define REP(i,n) for(ll i=0;i<n;i++)
#define FOR(i,a,b) for(ll i=a;i<b;i++)
#define FORR(i,a,b) for(ll i=b-1;i>=a;i--)

#define vl vector<ll>
#define pll pair<ll,ll>

#define DEBUG(x) cout<<#x<<": "<<x<<endl

using namespace std;
/*}}}*/

int main() {
  ll h,w;
  cin >> h >> w;
  ll cp = 1;
  ll cc = 0;
  bool eliminated = false;
  REP(i,h){
    if(eliminated){
      cout << -1 << endl;
      continue;
    }
    ll a,b;
    cin >> a >> b;
    if(cp>=a){
      if(b==w) {
        eliminated = true;
        cout << -1 << endl;
        continue;
      }
      if(i>0) cc += (b+1) - cp; 
      cp = b+1;
    }
    cc += 1;
    cout << cc << endl;
  }
  return 0;
}