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;
#define rep(i, n) for (int i = 0; i < (n); ++i)


int main() {
  int h, w; cin >> h >> w;

  set<pair<int, int>> S, T;
  rep(i, w) S.emplace(i, 0);
  rep(i, w) T.emplace(0, i);

  rep(k, h) {
    int a, b; cin >> a >> b;
    --a;

    auto l = S.lower_bound({a, -1});
    auto r = S.lower_bound({b, -1});

    int x = w;
    while (l != r) {
      auto [i, j] = *l;
      x = min(x, j-i+b);
      l = S.erase(l);
      T.erase({j, i});
    }

    if (x < w && b < w) S.emplace(b, x);
    if (x < w && b < w) T.emplace(x, b);

    int ans = -1;
    if (!T.empty()) ans = k+1 + T.begin()->first;
    cout << ans << '\n';
  }
}