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: Wrong Answer)

#define CPP17
#include <limits>
#include <initializer_list>
#include <utility>
#include <bitset>
#include <tuple>
#include <type_traits>
#include <functional>
#include <string>
#include <array>
#include <deque>
#include <list>
#include <queue>
#include <stack>
#include <vector>
#include <map>
#include <set>
#include <unordered_map>
#include <unordered_set>
#include <iterator>
#include <algorithm>
#include <complex>
#include <random>
#include <numeric>
#include <iostream>
#include <iomanip>
#include <sstream>
#include <regex>
#include <cassert>
#include <cstddef>
#ifdef CPP17
#include <variant>
#endif

#define endl codeforces

#define ALL(v) std::begin(v), std::end(v)
#define ALLR(v) std::rbegin(v), std::rend(v)

using ll = std::int64_t;
using ull = std::uint64_t;
using pii = std::pair<int, int>;
using tii = std::tuple<int, int, int>;
using pll = std::pair<ll, ll>;
using tll = std::tuple<ll, ll, ll>;
using size_type = ssize_t;
template <typename T> using vec = std::vector<T>;
template <typename T> using vvec = vec<vec<T>>;

template <typename T> const T& var_min(const T &t) { return t; }
template <typename T> const T& var_max(const T &t) { return t; }
template <typename T, typename... Tail> const T& var_min(const T &t, const Tail&... tail) { return std::min(t, var_min(tail...)); }
template <typename T, typename... Tail> const T& var_max(const T &t, const Tail&... tail) { return std::max(t, var_max(tail...)); }
template <typename T, typename... Tail> void chmin(T &t, const Tail&... tail) { t = var_min(t, tail...); }
template <typename T, typename... Tail> void chmax(T &t, const Tail&... tail) { t = var_max(t, tail...); }

template <typename T, std::size_t Head, std::size_t... Tail> 
struct multi_dim_array { using type = std::array<typename multi_dim_array<T, Tail...>::type, Head>; };

template <typename T, std::size_t Head> 
struct multi_dim_array<T, Head> { using type = std::array<T, Head>; };

template <typename T, std::size_t... Args> using mdarray = typename multi_dim_array<T, Args...>::type;

#ifdef CPP17
template <typename T, typename F, typename... Args> 
void fill_seq(T &t, F f, Args... args) { 
    if constexpr (std::is_invocable<F, Args...>::value) { 
        t = f(args...); 
    } else { 
        for (size_type i = 0; i < t.size(); i++) fill_seq(t[i], f, args..., i); 
    } 
}
#endif

template <typename T> vec<T> make_v(size_type sz) { return vec<T>(sz); }

template <typename T, typename... Tail> 
auto make_v(size_type hs, Tail&&... ts) { 
    auto v = std::move(make_v<T>(std::forward<Tail>(ts)...)); 
    return vec<decltype(v)>(hs, v); 
}

namespace init__ { 
struct InitIO { 
    InitIO() { 
        std::cin.tie(nullptr); 
        std::ios_base::sync_with_stdio(false); 
        std::cout << std::fixed << std::setprecision(30); 
    } 
} init_io; 
}
template <typename T>
T ceil_pow2(T bound) {
    T ret = 1;
    while (ret < bound) ret *= 2;
    return ret;
}
template <typename T>
T ceil_div(T a, T b) { return a / b + !!(a % b); }
#define CPP17


namespace utility {

template <typename T>
using validate_integer = typename std::enable_if<std::is_integral<T>::value, ll>::type;

template <typename T>
auto popcount(T n) -> validate_integer<T> {
    return __builtin_popcountll(n);
}

// 0 indexed
template <typename T>
auto msb(T n) -> validate_integer<T> {
    return 64 - __builtin_clzll(n) - 1;
}

}

namespace segtree {

template <typename M, typename Op>
class LazySegmentTree {
    struct segment {
        M m;
        Op op;
        bool has_lazy;

        segment(M m = M()) : m(m), op(Op()), has_lazy(false) { }

        void update_op(Op o) {
            m.apply(o);
            op = Op::merge(op, o);
            has_lazy = true;
        }

        void init_op() {
            op = Op();
            has_lazy = false;
        }
    };

    vec<segment> segs;
    size_type height;

    void push(size_type idx) {
        auto &s = segs[idx];
        if (!s.has_lazy) return;
        for (int i = 0; i < 2; i++) {
            auto cidx = 2 * idx + i;
            if (segs.size() <= cidx) break;
            auto &cs = segs[cidx];
            cs.update_op(s.op);
        }
        s.init_op();
    }

    void propagate_from_top(size_type idx) {
        for (int i = height; 1 <= i; i--) push(idx >> i);
    }

    void update_from_bottom(size_type idx) {
        while (true) {
            auto pidx = idx / 2;
            if (pidx == 0) break;
            size_type c0 = 2 * pidx + 0,
                      c1 = 2 * pidx + 1;
            push(c0); push(c1);
            segs[pidx].m = M::merge(segs[c0].m, segs[c1].m);
            idx = pidx;
        }
    }

    size_type get_endpoint_seg(size_type i) {
        i += size();
        return i / (i & -i);
    }

public:
    template <typename F>
    LazySegmentTree(F f, size_type sz) {
        size_type sz2 = ceil_pow2(sz);
        segs.resize(sz2 * 2);
        height = utility::msb(sz2);
        for (size_type i = 0; i < sz; i++) segs[i + sz2] = f(i);
        for (size_type i = sz2 - 1; 1 <= i; i--) segs[i] = M::merge(segs[2 * i].m, segs[2 * i + 1].m);
    }

    template <typename T>
    LazySegmentTree(const vec<T> &v) 
        : LazySegmentTree([&](size_type i) { return v[i]; }, v.size()) { }

    size_type size() const {
        return segs.size() / 2;
    }

    template <typename T>
    void update_query(size_type ql, size_type qr, const T &t) {
        Op op(t);
        auto l0 = get_endpoint_seg(ql);
        auto r0 = get_endpoint_seg(qr);
        propagate_from_top(l0);
        propagate_from_top(r0);
        size_type lnode = ql + size(), rnode = qr + size();
        while (lnode < rnode) {
            if (lnode & 1) {
                segs[lnode].update_op(op);
                push(lnode);
                lnode++;
            }
            if (rnode & 1) {
                rnode--;
                segs[rnode].update_op(op);
                push(rnode);
            }
            lnode /= 2;
            rnode /= 2;
        }
        update_from_bottom(l0);
        update_from_bottom(r0);
    }

    M get_query(ll ql, ll qr) {
        auto ret = M();
        auto l0 = get_endpoint_seg(ql);
        auto r0 = get_endpoint_seg(qr);
        propagate_from_top(l0);
        propagate_from_top(r0);
        size_type lnode = ql + size(), rnode = qr + size();
        while (lnode < rnode) {
            if (lnode & 1) {
                push(lnode);
                ret = M::merge(segs[lnode].m, ret);
                lnode++;
            }
            if (rnode & 1) {
                rnode--;
                push(rnode);
                ret = M::merge(ret, segs[rnode].m);
            }
            lnode /= 2;
            rnode /= 2;
        }
        return ret;
    }
};

}

const ll inf = 5e15;

struct Op {
    ll v;

    Op(ll v = -1) : v(v) { }

    static Op merge(Op a, Op b) {
        if (a.v == -1) return b;
        if (b.v == -1) return a;
        auto v = [&]() -> ll {
            if (a.v == inf) return inf;
            if (b.v == inf) return inf;
            return std::min(a.v, b.v);
        }();
        return Op(v);
    }
};

struct M {
    ll dist, i, l;

    M(ll dist, ll i, ll l) : dist(dist), i(i), l(l) { }
    M() : M(inf, inf, inf) { }

    static M merge(M a, M b) {
        ll dist = std::min(a.dist, b.dist);

        ll i = [&]() -> ll {
            bool aok = (a.l < inf);
            bool bok = (b.l < inf);
            if (aok && bok) return std::min(a.i, b.i);
            if (aok) return a.i;
            if (bok) return b.i;
            return inf;
        }();

        /*
        ll l = [&]() -> ll {
            bool aok = (a.l < inf);
            bool bok = (b.l < inf);
            if (aok && bok) return std::max(a.l, b.l);
            if (aok) return a.l;
            if (bok) return b.l;
            return inf;
        }();
        */
        ll l = std::max(a.l, b.l);
        return M(dist, i, l);
    }

    void apply(Op o) {
        if (o.v == inf) {
            l = inf;
        } else {
            chmin(l, o.v);
        }
        if (l == inf || i == inf) {
            dist = inf;
        } else {
            dist = i - l;
        }
    }
};

int main() {
    ll h, w;
    std::cin >> h >> w;
    vec<pll> lrv(h);
    for (auto &[ a, b ] : lrv) {
        std::cin >> a >> b;
        a--;
    }
    
    segtree::LazySegmentTree<M, Op> lst([&](ll i) { return M(0, i, i); }, w);
    for (ll i = 0; i < h; i++) {
        auto [ l, r ] = lrv[i];
        if (l == 0) {
            lst.update_query(l, r, Op(inf));
        } else {
            ll nl = lst.get_query(0, l).l;
            if (nl == inf) {
                lst.update_query(l, r, Op(inf));
            } else {
                lst.update_query(l, r, Op(nl));
            }
        }
        auto res = lst.get_query(0, w);
        ll ans = res.dist;
        ans += i + 1;
        if (inf <= ans) ans = -1;
        std::cout << ans << "\n";
    }

    return 0;
}