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 <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>
#include <cmath>
#include <climits>
#include <cassert>

#include <iostream>

#include <vector>
#include <queue>
#include <list>
#include <stack>
#include <deque>
#include <map>
#include <set>
#include <unordered_map>
#include <unordered_set>

#include <algorithm>
#include <utility>
#include <memory>
#include <bitset>
#include <string>
#include <tuple>
#include <functional>
using namespace std;

#define lowbit(x) ((x) & -(x))
#define lson l,mid,id<<1
#define rson mid+1,r,id<<1|1
#define ls id<<1
#define rs id<<1|1
#define MID(l,r) ((l)+(((r)-(l))>>1))
#define fi first
#define se second
#define mk make_pair
#define mt make_tuple
#define pb push_back
#define epb emplace_back
#define all(a) a.begin(),a.end()
#define rall(a) a.rbegin(),a.rend()

using LL = long long;
//using LL = __int64;
using pii = pair<int, int>;
using pdd = pair<double, double>;
using pLL = pair<LL, LL>;

const int INF = 0x3f3f3f3f;
const LL LINF = 0x3f3f3f3f3f3f3f3f;
const double DINF = 1e100;
const double pi = acos(-1.0);
const double eps = 1e-7;
const int e5 = 100000; // 1e5
const int e6 = 1000000; //1e6;
const int MOD_1e9 = 1000000007; //1e9 + 7
const int MOD_998 = 998244353;
const int MOD = MOD_1e9;

template< typename T > inline void get_min(T &x, T y) {if(y < x) x = y;}
template< typename T > inline void get_max(T &x, T y) {if(x < y) x = y;}
template< typename T > inline void get_unique(vector<T> &vec) {sort(all(vec)); vec.erase(unique(all(vec)), vec.end());}

inline int sig(double x) {return x < -eps ? -1 : eps < x;}
LL fp(LL a, LL n, LL mod = MOD)
{
    if(n < 0) a = fp(a, mod - 2, mod), n = -n;
    LL res = 1;
    for(; n; n >>= 1, a = a * a % mod)
        if(n & 1)
            res = res * a % mod;
    return res;
}

template< int mod > class Mint
{
public:
    int x;
    Mint():x(0) {}
    Mint(int _x): x(_x) {if(x < 0 || x >= mod) x %= mod; if(x < 0) x += mod;}
    Mint(LL _x) {if(_x < 0 || _x >= mod) _x %= mod; if(_x < 0) _x += mod; x = _x;}
    Mint operator () () {return x;}
    Mint operator - () const {return Mint(x == 0 ? x : mod - x);}
    Mint operator + (const Mint &rhs) const {return Mint(x + rhs.x >= mod ? x + rhs.x - mod : x + rhs.x);}
    Mint operator - (const Mint &rhs) const {return Mint(x - rhs.x < 0 ? x - rhs.x + mod : x - rhs.x);}
    Mint operator * (const Mint &rhs) const {return Mint((LL)x * rhs.x % mod);}
    Mint operator / (const Mint &rhs) const {return Mint((LL)x * fp(rhs.x, -1, mod) % mod);}
    bool operator == (const Mint &rhs) const {return x == rhs.x;}
    bool operator != (const Mint &rhs) const {return x != rhs.x;}
    Mint &operator += (const Mint &rhs) {x += rhs.x; if(x >= mod) x -= mod; return *this;}
    Mint &operator -= (const Mint &rhs) {x -= rhs.x; if(x < 0) x += mod; return *this;}
    Mint &operator *= (const Mint &rhs) {x = (LL)x * rhs.x % mod; return *this;}
    Mint &operator /= (const Mint &rhs) {x = (LL)x * fp(rhs.x, -1, mod) % mod; return *this;}
    friend ostream &operator << (ostream &out, const Mint &rhs) {return out << to_string(rhs.x);}
    Mint inv() {return Mint(fp(x, -1, mod));}
    Mint pow(int k) {return Mint(fp(x, k, mod));}
};

class fast_reader
{
private:
    int buff_size;
    char *buff_ptr;
    char *ptr;
    char *tail;
    bool is_open;
    fast_reader(const fast_reader &) = delete;
    fast_reader &operator = (const fast_reader &) = delete;

    inline bool is_digit() const {return '0' <= *ptr && *ptr <= '9';}
    inline bool is_blank() const {return *ptr == ' ' || *ptr == '\n' || *ptr == '\t' || *ptr == '\0';}
    template <typename T> inline void read_i(T &x)
    {
        bool f = false;
        x = 0;
        while(ptr < tail && !is_digit()) {if(*ptr == '-') f = true; ptr++;}
        while(ptr < tail && is_digit()) {x = (x << 1) + (x << 3) + (*ptr & 0xf); ptr++;}
        if(f) x = -x;
    }
    template <typename T> inline void read_f(T &x)
    {
        static char t_buff[1 << 6];
        read(t_buff);
        x = atof(t_buff);
    }
public:
    fast_reader(): buff_size(0), buff_ptr(nullptr), ptr(nullptr), tail(nullptr), is_open(false) {}
    ~fast_reader() {if(is_open) free(buff_ptr);}
    template <typename T> fast_reader &operator >> (T &x) {read(x); return *this;}

    inline void open_alter(int _base_size = 1 << 24) //2^24B = 16MB
    {
        if(is_open)
            throw runtime_error("fast reader is reopened!");

        int input_size = 0;
        int call_size = _base_size;
        buff_ptr = (char *) malloc(call_size);
        input_size += fread(buff_ptr, 1, call_size, stdin);
        while(feof(stdin) == 0)
        {
            int recall_size = call_size;
            buff_ptr = (char *) realloc(buff_ptr, call_size + recall_size);
            tail = buff_ptr + call_size;
            input_size += fread(tail, 1, recall_size, stdin);
            call_size += recall_size;
        }
        buff_ptr = (char *) realloc(buff_ptr, input_size);
        ptr = buff_ptr;
        tail = buff_ptr + input_size;
        buff_size = input_size;
        is_open = true;
    }

    template<typename T, typename ...Args> inline void read(T &x, Args &...args) {read(x); read(args...);}
    inline void read(int &x) {read_i(x);}
    inline void read(unsigned &x) {read_i(x);}
    inline void read(long long &x) {read_i(x);}
    inline void read(unsigned long long &x) {read_i(x);}
    inline void read(float &x) {read_f(x);}
    inline void read(double &x) {read_f(x);}
    inline void read(char *str)
    {
        while(ptr < tail && is_blank()) ptr++;
        while(ptr < tail && !is_blank()) *str = *ptr++, str++;
        *str = '\0';
    }
    inline void read(string &s)
    {
        while(ptr < tail && is_blank()) ptr++;
        char *pre = ptr;
        while(ptr < tail && !is_blank()) ptr++;
        s = std::move(string(pre, ptr)); //C++11 #include<utility> -> move : return a rvalue
    }

    inline bool is_end()
    {
        while(ptr < tail && is_blank()) ptr++;
        return ptr >= tail;
    }
}reader;

const int maxn = (int) 2e5 + 5;
const int maxm = (int) 5e6 + 5;

int n, m;
int ans[maxn];
int T[maxn << 2];
int f[maxn << 2];
pii p[maxn << 2];

void lazy(int id)
{
    if(f[id] == -1) return ;
    int x = f[id];
    f[id] = -1;
    T[ls] = T[rs] = f[ls] = f[rs] = x;
    p[ls].fi = p[rs].fi = INF;
}

void mer(int id)
{
    T[id] = min(T[ls], T[rs]);
    p[id] = p[rs].fi == INF ? p[ls] : p[rs];
}

void build(int l, int r, int id)
{
    f[id] = -1;
    if(l == r)
    {
        T[id] = 0;
        p[id] = mk(0, l);
        return ;
    }
    int mid = MID(l, r);
    build(lson);
    build(rson);
    mer(id);
}

void upd(int t, int v, int l, int r, int id)
{
    if(l == r)
    {
        get_min(T[id], v);
        p[id] = mk(T[id], l);
        return ;
    }
    lazy(id);
    int mid = MID(l, r);
    if(t <= mid) upd(t, v, lson);
    else upd(t, v, rson);
    mer(id);
}

pii que(int L, int R, int l, int r, int id)
{
    if(L <= l && r <= R) return p[id];
    lazy(id);
    int mid = MID(l, r);
    if(mid < R)
    {
        pii t = que(L, R, rson);
        if(t.fi != INF) return t;
    }
    if(L <= mid)
    {
        return que(L, R, lson);
    }
    return mk(INF, -1);
}

void ers(int L, int R, int l, int r, int id)
{
    if(L <= l && r <= R)
    {
        T[id] = INF;
        f[id] = INF;
        p[id].fi = INF;
        return ;
    }
    lazy(id);
    int mid = MID(l, r);
    if(L <= mid) ers(L, R, lson);
    if(mid < R) ers(L, R, rson);
    mer(id);
}

void work()
{
    reader >>n >>m;
    build(1, m, 1);

    for(int i = 1; i <= n; i++)
    {
        int l, r;
        reader >>l >>r;
        pii t = que(l, r, 1, m, 1);
        ers(l, r, 1, m, 1);
        if(t.fi != INF)
        {
            if(r + 1 <= m)
                upd(r + 1, t.fi + (r + 1 - t.se), 1, m, 1);
        }
        ans[i] = i + T[1];
        if(ans[i] >= INF) ans[i] = -1;
    }

    for(int i = 1; i <= n; i++)
        printf("%d\n", ans[i]);
}

int main()
{
#ifdef yukihana0416
freopen("in.txt", "r", stdin);
//freopen("out.txt", "w", stdout);
#endif // yukihana0416
    reader.open_alter(1 << 24);

    int tc = 1;
//    reader >> tc;
    for(int ca = 1; ca <= tc; ca++)
    {
//        printf("Case #%d: ", ca);
//        printf("Case #%d:\n", ca);
        work();
    }
    return 0;
}