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 rep(i,n) for (int i = 0; i < (int)(n); i ++)
#define irep(i,n) for (int i = (int)(n) - 1;i >= 0;--i)
using namespace std;
using ll = long long;
using PL = pair<ll,ll>;
using P = pair<int,int>;
constexpr int INF = 1000000000;
constexpr long long HINF = 1000000000000000;
constexpr long long MOD = 1000000007;// = 998244353;
constexpr double EPS = 1e-4;
constexpr double PI = 3.14159265358979;

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

    int H,W; cin >> H >> W;

    map<int,int> mp;
    multiset<int> st;
    rep(i,W) mp[i] = i;
    rep(i,W) st.insert(0);

    rep(i,H) {
        int l,r; cin >> l >> r;
        --l;
        auto itr = mp.lower_bound(l);
        int rr = -1;
        while (itr != mp.end() && itr->first <= r){
            rr = max(rr,itr->second);
            int v = (*itr).first - (*itr).second;
            st.erase(st.find(v));
            mp.erase(itr++);
        }
        if (rr != -1 && r < W) {
            mp[r] = rr;
            st.insert(r - rr);
        }
        int ans = -1;
        if ((int)st.size() > 0) {
            ans = *st.begin() + i + 1;
        }
        cout << ans << '\n';
    }
    return 0;
}