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 Int = long long;  // clang-format off
#define REP_(i, a_, b_, a, b, ...) for (Int i = (a), lim##i = (b); i < lim##i; i++)
#define REP(i, ...) REP_(i, __VA_ARGS__, __VA_ARGS__, 0, __VA_ARGS__)
#define ALL(v) std::begin(v), std::end(v)
struct SetupIO { SetupIO() { std::cin.tie(nullptr), std::ios::sync_with_stdio(false), std::cout << std::fixed << std::setprecision(13); } } setup_io;
#ifndef dump
#define dump(...)
#endif  // clang-format on

/**
 *    author:  knshnb
 *    created: Tue Sep  1 20:36:57 JST 2020
 **/

signed main() {
    Int H, W;
    std::cin >> H >> W;
    std::map<Int, Int> mp;
    std::multiset<Int> s;
    REP(j, W) mp[j] = j, s.insert(0);
    REP(i, H) {
        Int l, r;
        std::cin >> l >> r, l--;
        Int x = -1;
        auto it = mp.lower_bound(l);
        while (it != mp.end() && it->first <= r) {
            x = it->second;
            s.erase(s.find(it->first - it->second));
            mp.erase(it++);
        }
        if (r != W && x != -1) mp[r] = x, s.insert(r - x);
        std::cout << (s.size() ? i + 1 + *s.begin() : -1) << "\n";
    }
}