Problem:
Score : 600 points

Problem Statement

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.

Sample Input 1

4 4
2 4
1 1
2 3
2 4

Sample Output 1

1
3
6
-1

Let (i,j) denote the square at the i-th row from the top and j-th column from the left.

For k=1, we need one move such as (1,1) → (2,1).

For k=2, we need three moves such as (1,1) → (2,1) → (2,2) → (3,2).

For k=3, we need six moves such as (1,1) → (2,1) → (2,2) → (3,2) → (3,3) → (3,4) → (4,4).

For k=4, it is impossible to reach any square in the fifth row from the top.

Solution in C++ (GCC 9.2.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
#define lson root<<1,l,midd
#define rson root<<1|1,midd+1,r
const int M=2e5+5;
const int inf=0x3f3f3f3f;
const ll INF=1e18;
struct Segtree{
    ll tr[M<<2],lz[M<<2];
    void build(int root,int l,int r){
        tr[root]=0,lz[root]=0;
        if(l==r)
            return ;
        int midd=(l+r)>>1;
        build(lson);
        build(rson);
    }
    void pushdown(int root){
        ll c=lz[root];
        tr[root<<1]+=c,tr[root<<1|1]+=c;
        lz[root<<1]+=c,lz[root<<1|1]+=c;
        lz[root]=0;
    }
    void update(int L,int R,ll val,int root,int l,int r){
        if(L<=l&&r<=R){
            tr[root]+=val;
            lz[root]+=val;
            return ;
        }
        if(lz[root])
            pushdown(root);
        int midd=(l+r)>>1;
        if(L<=midd)
            update(L,R,val,lson);
        if(R>midd)
            update(L,R,val,rson);
        tr[root]=min(tr[root<<1],tr[root<<1|1]);
    }
    ll query(int L,int R,int root,int l,int r){
        if(L<=l&&r<=R){
            return tr[root];
        }
        if(lz[root])
            pushdown(root);
        ll res=INF;
        int midd=(l+r)>>1;
        if(L<=midd)
            res=min(res,query(L,R,lson));
        if(R>midd)
            res=min(res,query(L,R,rson));
        return res;
    }
}x,y;
int main(){
    int n,m;
    scanf("%d%d",&n,&m);
    x.build(1,1,m),y.build(1,1,m);
    for(int i=1;i<=m;i++)
        y.update(i,i,-i,1,1,m);
    for(int i=1;i<=n;i++){
        int a,b;
        scanf("%d%d",&a,&b);
        ///b+1
        x.update(b+1,b+1,min(1ll*(b+1+y.query(1,b,1,1,m))-x.query(b+1,b+1,1,1,m),0ll),1,1,m);
        y.update(b+1,b+1,min(y.query(1,b,1,1,m)-y.query(b+1,b+1,1,1,m),0ll),1,1,m);
        ///a~b
        x.update(a,b,1e9,1,1,m);
        y.update(a,b,1e9,1,1,m);
        ///向下
        x.update(1,m,1,1,1,m);
        y.update(1,m,1,1,1,m);
        ll ans=x.query(1,m,1,1,m);
        if(ans>=1e9)
            puts("-1");
        else
            printf("%lld\n",ans);
    }
    return 0;
}