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: Time Limit Exceeded)

#include<bits/stdc++.h>

#define si(a) scanf("%d",&a)
#define sl(a) scanf("%lld",&a)
#define sd(a) scanf("%lf",&a)
#define sc(a) scahf("%c",&a);
#define ss(a) scanf("%s",a)
#define pi(a) printf("%d\n",a)
#define pl(a) printf("%lld\n",a)
#define pc(a) putchar(a)
#define ms(a) memset(a,0,sizeof(a))
#define repi(i, a, b) for(register int i=a;i<=b;++i)
#define repd(i, a, b) for(register int i=a;i>=b;--i)
#define reps(s) for(register int i=head[s];i;i=Next[i])
#define ll long long
#define ull unsigned long long
#define vi vector<int>
#define pii pair<int,int>
#define mii unordered_map<int,int>
#define msi unordered_map<string,int>
#define lowbit(x) ((x)&(-(x)))
#define ce(i, r) i==r?'\n':' '
#define pb push_back
#define fi first
#define se second
#define all(x) x.begin(),x.end()
#define INF 0x3f3f3f3f
#define pr(x) cout<<#x<<": "<<x<<endl
using namespace std;

inline int qr() {
    int f = 0, fu = 1;
    char c = getchar();
    while (c < '0' || c > '9') {
        if (c == '-')fu = -1;
        c = getchar();
    }
    while (c >= '0' && c <= '9') {
        f = (f << 3) + (f << 1) + c - 48;
        c = getchar();
    }
    return f * fu;
}


const int N = 4e5 + 10;

struct Seg_Tree {
    struct T {
        int l, r, ans, add;
    } t[N * 4];

    void build(int p, int l, int r) {
        t[p].l = l, t[p].r = r, t[p].ans = t[p].add = 0;
        if (l == r)return;
        int mid = (l + r) >> 1;
        build(p << 1, l, mid);
        build(p << 1 | 1, mid + 1, r);
    }

    void spread(int p) {
        if (t[p].add) {
            t[p << 1].ans = t[p].l - t[p].add;
            t[p << 1].add = t[p].add;
            t[p << 1 | 1].ans = ((t[p].l + t[p].r) >> 1) + 1 - t[p].add;
            t[p << 1 | 1].add = t[p].add;
            t[p].add = 0;
        }
    }

    void change(int p, int l, int r, int c) {
        //if (t[p].r < l || t[p].l > r)return;
        if (l <= t[p].l && t[p].r <= r) {
            t[p].ans = l - c, t[p].add = c;
            return;
        }
        spread(p);
        int mid = (t[p].l + t[p].r) >> 1;
        if (l <= mid)change(p << 1, l, r, c);
        if (r > mid)change(p << 1 | 1, l, r, c);
        t[p].ans = min(t[p << 1].ans, t[p << 1 | 1].ans);
    }

    int ask(int p, int x) {
        if (t[p].l == t[p].r)return x - t[p].ans;
        spread(p);
        int mid = (t[p].l + t[p].r) >> 1;
        return x <= mid ? ask(p >> 1, x) : ask(p << 1 | 1, x);
    }
} tr;

int n, m, now = 1;

int main() {
    n = qr(), m = qr();
    tr.build(1, 1, m);
    repi(i, 1, n) {
        int l = qr(), r = qr();
        if (now >= l && now <= r)tr.change(1, now, r, -INF), now = r + 1;
        else if (now < l)tr.change(1, l, r, tr.ask(1, l - 1));
        if (now > m) {
            repi(j, i, n)puts("-1");
            return 0;
        }
        pi(i + tr.t[1].ans);
    }
    return 0;
}