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>
using namespace std;
using ll = long long;
using ull = unsigned long long;
//#define ll long long
template<class T> bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<class T> bool chmin(T &a, const T &b) { if (a>b) { a=b; return 1; } return 0; }
#define rep(i, n) REP(i, 0, n)
#define rep_rev(i, n) for (int (i) = (int)(n) - 1 ; (i) >= 0 ; --(i))
#define ALL(v) v.begin(), v.end()
#define MSG(a) cout << #a << " " << a << endl;
#define REP(i, x, n) for(int i = x; i < n; i++)
#define all(x) (x).begin(),(x).end()
ll t1,t2,t3;
const ll mod = 1000000007;
const int INF = 1e9;
const ll INFLONG = 1e18;

int main(){
  ll h,w;
  cin >> h >> w;
  vector<pair<ll,ll>> vec(h);
  rep(i,h){
    cin >> t1 >> t2;
    t1--,t2--;
    vec[i].first = t1;
    vec[i].second = t2;
  }
  vector<ll> score(w,0);
  vector<ll> ans(h,INFLONG);
  // vector<ll> visited(h,0);
  // rep(i,h){
  //   visited[i] = i;
  // }
  // rep(i,h){
  //   t1 = vec[i].second+1;
  //   REP(j,vec[i].first,vec[i].second+1){
  //     if(visited[j] < t1){
  //       visited[j] = t1;
  //       t1--;
  //     }else{
  //       break;
  //     }
  //   }
  // }
  // map<ll,ll> mp;
  // rep(i,h){
  //   mp[i] = i;
  // }
  rep(k,h){
    ll piv = k;
    rep(i,h){
      if(vec[i].first <= piv && piv <= vec[i].second){
        piv = vec[i].second+1;
      }
      if(piv < w){
        chmin(ans[i],i + 1 + piv - k);
      }else{
        break;
      }
    }
  }
  rep(i,h){
    if(ans[i] == INFLONG){
      ans[i] = -1;
    }
    cout << ans[i] << endl;
  }
}