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 namespace std;
#define MOD 1000000007
//#define MOD 998244353
#define INF 1000000010
#define EPS 1e-9
#define F first
#define S second

#define debug(x) cout<<x<<endl;
#define repi(i,x,n) for(int i=x;i<n;i++)
#define rep(i,n) repi(i,0,n)
#define lp(i,n) repi(i,0,n)
#define repn(i,n) for(int i=n;i>=0;i--)
//#define int long long
#define endl "\n"

typedef pair<int,int> PII;
typedef pair<int,string> PIS;
typedef pair<string,int> PSI;


signed main(){
  cin.tie(0);	
  ios::sync_with_stdio(false);

  
  int h,w;
  cin>>h>>w;
  set<PII> st;
  multiset<int> x;
  rep(i,w){
    st.insert(make_pair(i+1,i+1));
    x.insert(0);
  }
  st.insert({-1,(-1)*INF});
  x.insert(INF);
  st.insert({w+1,w+1});
  rep(i,h){
    int a,b,p;
    cin>>a>>b;
    while(1){
      auto itr=st.lower_bound({a,0});
      if(itr->F > b) break;
      if(next(itr)->F <= b+1){
	x.erase(x.find(itr->F - itr->S));
	st.erase(itr);
      }else{
	p=itr->S;
	x.erase(x.find(itr->F - itr->S));
	st.erase(itr);
	st.insert({b+1,p});
	x.insert({b+1-p});
      }
    }
    p=(*x.begin())+i+1;
    if(p>=h+w) p=-1;
    cout<<p<<endl;
  }
		  

  return 0;
}