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 <iostream>
#include <vector>
#include <set>

constexpr int INF = 1 << 30;

void solve() {
    int h, w;
    std::cin >> h >> w;

    std::set<int> s;
    for (int x = 0; x < w; ++x) s.insert(x);
    std::vector<int> ds(w, 0);

    std::multiset<int> dss;
    for (auto d : ds) dss.insert(d);

    for (int i = 1; i <= h; ++i) {
        int l, r;
        std::cin >> l >> r;
        --l;

        auto it = s.lower_bound(l);
        int min = INF;
        while (it != s.end() && *it <= r) {
            int x = *it;
            it = s.erase(it);

            dss.erase(dss.find(ds[x]));
            min = std::min(min, ds[x] + r - x);
            ds[x] = INF;
        }

        if (r < w && min < INF) {
            ds[r] = std::min(ds[r], min);
            s.insert(r);
            dss.insert(ds[r]);
        }

        if (dss.empty()) {
            std::cout << -1 << "\n";
        } else {
            int d = *dss.begin();
            std::cout << d + i << "\n";
        }
    }
}

int main() {
    std::cin.tie(nullptr);
    std::ios::sync_with_stdio(false);

    solve();

    return 0;
}