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 vi=vector<int>;
using vvi=vector<vi>;
using vl=vector<ll>;
using vvl=vector<vl>;
using vb=vector<bool>;
using vvb=vector<vb>;
using vc=vector<char>;
using vvc=vector<vc>;
using pii = pair<int,int>;
using pil = pair<int,ll>;
using pli = pair<ll,int>;
using pll = pair<ll,ll>;
using tiii = tuple<int,int,int>;
using vpii = vector<pii>;
using vpil = vector<pil>;
using vpli = vector<pli>;
using vpll = vector<pll>;

#define rep(i, n) for(int i=0;i<(int)n;i++)
#define rep2(i, s, n) for(int i=(s);i<(int)n;i++)
int INF=1e9+7;

int main() {
  int H,W;
  cin >> H >> W;
  vi A(H),B(H);
  rep(i,H) {
    cin >> A[i] >> B[i];
    A[i]--;B[i]--;
  }
  vi ans(H,-1),left(H+1);
  rep(k,H) {
    if(A[k]<=left[k]&&left[k]<=B[k]) left[k+1]=B[k]+1;
    else left[k+1]=left[k];
    if(left[k+1]>=W) break;
    ans[k]=k+1+left[k+1];
  }
  
  rep(k,H) cout << ans[k] << endl;
}