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;
const int N=2e5+5;
int n,m,ans[N],a[N],b[N],t[N<<2],t1[N<<2],t2[N<<2];
void update(int l,int r,int k)
{
    t1[k]=t[k]+r-l;t2[k]=t[k];
    if(l!=r)
    {
        int m=l+r>>1;
        t[k<<1]=t[k];t[k<<1|1]=t[k]+m+1-l;
    }
    t[k]=0;
}
int query(int l,int r,int k,int x)
{
    if(t[k]) update(l,r,k);
    if(l>x) return m+1;
    if(r<=x) return t1[k];
    int m=l+r>>1;
    int a=query(l,m,k<<1,x),b=query(m+1,r,k<<1|1,x);
    if(x<=r) a+=x>=m?x-m:0;
    else a+=r-m;
    t2[k]=min(t2[k<<1],t2[k<<1|1]);
    t1[k]=min(t1[k<<1]+r-m,t1[k<<1|1]);
    return min(a,b);
}
void update(int l,int r,int k,int x,int y,int d)
{
    if(t[k]) update(l,r,k);
    if(r<x||l>y) return;
    if(l>=x&&r<=y)
    {
        t[k]=d+l-x;
        update(l,r,k);
        return;
    }
    int m=l+r>>1;
    update(l,m,k<<1,x,y,d);update(m+1,r,k<<1|1,x,y,d);
    t2[k]=min(t2[k<<1],t2[k<<1|1]);
    t1[k]=min(t1[k<<1]+r-m,t1[k<<1|1]);
}
int main()
{
    scanf("%d%d",&n,&m);
    for(register int i=1,a,b,d;i<=n;i++)
    {
        scanf("%d%d",&a,&b);
        d=min(m+1,query(1,m,1,a-1)+1);
        update(1,m,1,a,b,d);
        printf("%d\n",t2[1]>=m?-1:t2[1]+i);
    }
}