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;
map<int, int> m;
multiset<int> s;
int main(){
    int h, w, a, b;
    cin >> h >> w;
    for (int i = 0; i < w; i++)
        m[i] = i, s.insert(0);
    for (int i = 0; i < h; i++){
        cin >> a >> b;
        a--;
        auto pos = m.lower_bound(a);
        int mx = -1;
        while (pos != m.end() && pos->first <= b){
            mx = max(mx, pos->second);
            int x = pos->first - pos->second;
            s.erase(s.find(x));
            m.erase(pos++);
        }
        if (mx != -1 && b < w){
            s.insert(b - mx);
            m[b] = mx;
        }
        cout << (s.empty() ? -1 : *s.begin() + i + 1) << endl;
    }
    return 0;
}