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>
#define fi first
#define se second
#define pb push_back
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;

int a[200010], b[200010];
multiset<int> ms;
set<pii> s;

int main() {
    ios_base::sync_with_stdio(0);
    int h, w; cin >> h >> w;
    for (int i=0;i<h;i++) {
        cin >> a[i] >> b[i];
        a[i]--; b[i]--;
    }
    for (int i=0;i<w;i++) {
        s.insert({i, i});
        ms.insert(0);
    }
    for (int i=0;i<h;i++) {
        auto st = s.lower_bound({a[i], -1});
        auto ed = s.lower_bound({b[i]+1, w});
        vector<pii> t;
        for (auto j=st;j!=ed;j++) {
            t.pb({j->se, j->fi});
            ms.erase(ms.find(j->fi-j->se));
        }
        s.erase(st, ed);

        if (t.size()) {
            pii p = *max_element(t.begin(), t.end());
            if (b[i]+1<w) {
                s.insert({b[i]+1, p.fi});
                ms.insert(b[i]+1-p.fi);
            }
        }
        cout << (ms.size()? *ms.begin()+i+1: -1) << endl;
    }
}