Problem: 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.

Example

Input

4 4
2 4
1 1
2 3
2 4


Output

1
3
6
-1

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  
  int h, w;
  cin >> h >> w;
  
  map<int, int> mp; // mp[now] = start
  multiset<int> ms; // multiset of (now - start)
  for (int i = 0; i < w; i++) {
    mp[i] = i;
    ms.insert(0);
  }
  mp[2e8] = 1e8; // sentinel
  ms.insert(1e8); // sentinel
  
  for (int i = 0; i < h; i++) {
    int a, b;
    cin >> a >> b;
    a--;
    auto it1 = mp.lower_bound(a);
    auto it2 = mp.lower_bound(b);
    if (it1 != it2) {
      int start, now;
      auto it = it1;
      while (it != it2) {
        start = it->second;
        now = it->first;
        int start2 = it->second, now2 = it->first;
        ms.erase(ms.find(now2 - start2));
        it = mp.erase(it);
      }
      if (b < w) {
        now = b;
        if (mp.find(now) == mp.end()) {
          mp[now] = start;
          ms.insert(now - start);
        }
      }
    }
    if (*(ms.begin()) == 1e8) cout << -1 << '\n';
    else cout << *(ms.begin()) + i + 1 << '\n';
  }
}