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 ll long long
#define Rep(i,l,r) for(int (i)=(l);(i)<=(r);(i)++)
using namespace std;
map<int,ll>::iterator it;
map<int,ll> mp;
multiset<ll> values;
int n,m,l,r;

int main(){
	cin>>n>>m;
	Rep(i,1,m){mp[i]=0;values.insert(0);}
	Rep(i,1,n){
		cin>>l>>r;
		if(r!=m){
			it=mp.upper_bound(r+1);
			if(it!=mp.begin()){
				it--;
				if(it->first!=r+1){
					ll v=it->second+(r+1-it->first);
					mp[r+1]=v;values.insert(v);
				}
			}
		}
		it=mp.lower_bound(l);
		while(it!=mp.end()&&it->first<=r){
			values.erase(values.find(it->second));
			it=mp.erase(it);
		}
		cout<<((values.size())?(i+(*values.begin())):(-1))<<endl;
	}
	return 0;
}