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 Rust (1.42.0) (judge verdict: Accepted)

pub trait Zero: PartialEq + Sized {
    fn zero() -> Self;
    #[inline]
    fn is_zero(&self) -> bool {
        self == &Self::zero()
    }
}
pub trait One: PartialEq + Sized {
    fn one() -> Self;
    #[inline]
    fn is_one(&self) -> bool {
        self == &Self::one()
    }
}
macro_rules !zero_one_impls {($({$Trait :ident $method :ident $($t :ty ) *,$e :expr } ) *) =>{$($(impl $Trait for $t {#[inline ] fn $method () ->Self {$e } } ) *) *} ;}
zero_one_impls !({Zero zero u8 u16 u32 u64 usize i8 i16 i32 i64 isize u128 i128 ,0 } {Zero zero f32 f64 ,0. } {One one u8 u16 u32 u64 usize i8 i16 i32 i64 isize u128 i128 ,1 } {One one f32 f64 ,1. } ) ;
pub trait IterScan: Sized {
    type Output;
    fn scan<'a, I: Iterator<Item = &'a str>>(iter: &mut I) -> Option<Self::Output>;
}
pub trait MarkedIterScan: Sized {
    type Output;
    fn mscan<'a, I: Iterator<Item = &'a str>>(self, iter: &mut I) -> Option<Self::Output>;
}
#[derive(Debug)]
pub struct Scanner<'a> {
    iter: std::str::SplitAsciiWhitespace<'a>,
}
impl<'a> Scanner<'a> {
    #[inline]
    pub fn new(s: &'a str) -> Self {
        let iter = s.split_ascii_whitespace();
        Self { iter }
    }
    #[inline]
    pub fn scan<T: IterScan>(&mut self) -> <T as IterScan>::Output {
        T::scan(&mut self.iter).unwrap()
    }
    #[inline]
    pub fn mscan<T: MarkedIterScan>(&mut self, marker: T) -> <T as MarkedIterScan>::Output {
        marker.mscan(&mut self.iter).unwrap()
    }
    #[inline]
    pub fn scan_vec<T: IterScan>(&mut self, size: usize) -> Vec<<T as IterScan>::Output> {
        (0..size)
            .map(|_| T::scan(&mut self.iter).unwrap())
            .collect()
    }
    #[inline]
    pub fn scan_chars(&mut self) -> Vec<char> {
        self.iter.next().unwrap().chars().collect::<Vec<char>>()
    }
    #[inline]
    pub fn scan_chars_with(&mut self, base: char) -> Vec<usize> {
        self.iter
            .next()
            .unwrap()
            .chars()
            .map(|c| (c as u8 - base as u8) as usize)
            .collect::<Vec<usize>>()
    }
}
mod scanner_impls {
    use super::*;
    macro_rules !iter_scan_impls {($($t :ty ) *) =>{$(impl IterScan for $t {type Output =Self ;#[inline ] fn scan <'a ,I :Iterator <Item =&'a str >>(iter :&mut I ) ->Option <Self >{iter .next () ?.parse ::<$t >() .ok () } } ) *} ;}
    iter_scan_impls !(char u8 u16 u32 u64 usize i8 i16 i32 i64 isize f32 f64 u128 i128 String ) ;
    macro_rules !iter_scan_tuple_impl {($($T :ident ) *) =>{impl <$($T :IterScan ) ,*>IterScan for ($($T ,) *) {type Output =($(<$T as IterScan >::Output ,) *) ;#[inline ] fn scan <'a ,It :Iterator <Item =&'a str >>(_iter :&mut It ) ->Option <Self ::Output >{Some (($($T ::scan (_iter ) ?,) *) ) } } } ;}
    iter_scan_tuple_impl!();
    iter_scan_tuple_impl!(A);
    iter_scan_tuple_impl !(A B ) ;
    iter_scan_tuple_impl !(A B C ) ;
    iter_scan_tuple_impl !(A B C D ) ;
    iter_scan_tuple_impl !(A B C D E ) ;
    iter_scan_tuple_impl !(A B C D E F ) ;
    iter_scan_tuple_impl !(A B C D E F G ) ;
    iter_scan_tuple_impl !(A B C D E F G H ) ;
    iter_scan_tuple_impl !(A B C D E F G H I ) ;
    iter_scan_tuple_impl !(A B C D E F G H I J ) ;
    iter_scan_tuple_impl !(A B C D E F G H I J K ) ;
    pub struct ScannerIter<'a, 'b, T> {
        inner: &'b mut Scanner<'a>,
        _marker: std::marker::PhantomData<fn() -> T>,
    }
    impl<'a, 'b, T: IterScan> Iterator for ScannerIter<'a, 'b, T> {
        type Item = <T as IterScan>::Output;
        fn next(&mut self) -> Option<Self::Item> {
            T::scan(&mut self.inner.iter)
        }
    }
    impl<'a> Scanner<'a> {
        #[inline]
        pub fn iter<'b, T: IterScan>(&'b mut self) -> ScannerIter<'a, 'b, T> {
            ScannerIter {
                inner: self,
                _marker: std::marker::PhantomData,
            }
        }
    }
}
pub mod marker {
    use super::*;
    pub struct Usize1;
    impl IterScan for Usize1 {
        type Output = usize;
        #[inline]
        fn scan<'a, I: Iterator<Item = &'a str>>(iter: &mut I) -> Option<Self::Output> {
            usize::scan(iter).map(|x| x.wrapping_sub(1))
        }
    }
    pub struct Isize1;
    impl IterScan for Isize1 {
        type Output = isize;
        #[inline]
        fn scan<'a, I: Iterator<Item = &'a str>>(iter: &mut I) -> Option<Self::Output> {
            isize::scan(iter).map(|x| x.wrapping_sub(1))
        }
    }
}
#[macro_export]
macro_rules !min {($e :expr ) =>{$e } ;($e :expr ,$($es :expr ) ,+) =>{std ::cmp ::min ($e ,min !($($es ) ,+) ) } ;}
#[macro_export]
macro_rules !chmin {($dst :expr ,$($src :expr ) ,+) =>{{let x =std ::cmp ::min ($dst ,min !($($src ) ,+) ) ;$dst =x ;} } ;}
#[macro_export]
macro_rules !max {($e :expr ) =>{$e } ;($e :expr ,$($es :expr ) ,+) =>{std ::cmp ::max ($e ,max !($($es ) ,+) ) } ;}
#[macro_export]
macro_rules !chmax {($dst :expr ,$($src :expr ) ,+) =>{{let x =std ::cmp ::max ($dst ,max !($($src ) ,+) ) ;$dst =x ;} } ;}
/// binary operaion: $T \circ T \to T$
pub trait Magma {
    /// type of operands: $T$
    type T: Clone + PartialEq;
    /// binary operaion: $\circ$
    fn operate(&self, x: &Self::T, y: &Self::T) -> Self::T;
    #[inline]
    fn reverse_operate(&self, x: &Self::T, y: &Self::T) -> Self::T {
        self.operate(y, x)
    }
}
/// $\forall a,\forall b,\forall c \in T, (a \circ b) \circ c = a \circ (b \circ c)$
pub trait Associative {}
/// associative binary operation
pub trait SemiGroup: Magma + Associative {}
impl<S: Magma + Associative> SemiGroup for S {}
/// $\exists e \in T, \forall a \in T, e \circ a = a \circ e = e$
pub trait Unital: Magma {
    /// identity element: $e$
    fn unit(&self) -> Self::T;
}
/// associative binary operation and an identity element
pub trait Monoid: SemiGroup + Unital {
    /// binary exponentiation: $x^n = x\circ\ddots\circ x$
    fn pow(&self, x: Self::T, n: usize) -> Self::T {
        let mut n = n;
        let mut res = self.unit();
        let mut base = x;
        while n > 0 {
            if n & 1 == 1 {
                res = self.operate(&res, &base);
            }
            base = self.operate(&base, &base);
            n = n >> 1;
        }
        res
    }
}
impl<M: SemiGroup + Unital> Monoid for M {}
/// $\exists e \in T, \forall a \in T, \exists b,c \in T, b \circ a = a \circ c = e$
pub trait Invertible: Magma {
    /// $a$ where $a \circ x = e$
    fn inverse(&self, x: &Self::T) -> Self::T;
    #[inline]
    fn rinv_operate(&self, x: &Self::T, y: &Self::T) -> Self::T {
        self.operate(x, &self.inverse(y))
    }
}
/// associative binary operation and an identity element and inverse elements
pub trait Group: Monoid + Invertible {}
impl<G: Monoid + Invertible> Group for G {}
/// $\forall a,\forall b \in T, a \circ b = b \circ a$
pub trait Commutative {}
/// commutative monoid
pub trait AbelianMonoid: Monoid + Commutative {}
impl<M: Monoid + Commutative> AbelianMonoid for M {}
/// commutative group
pub trait AbelianGroup: Group + Commutative {}
impl<G: Group + Commutative> AbelianGroup for G {}
/// $\forall a \in T, a \circ a = a$
pub trait Idempotent {}
/// idempotent monoid
pub trait IdempotentMonoid: Monoid + Idempotent {}
impl<M: Monoid + Idempotent> IdempotentMonoid for M {}
#[derive(Clone, Debug)]
pub struct MonoidalOperation<T: Clone + PartialEq, F: Fn(&T, &T) -> T> {
    e: T,
    op: F,
}
mod monoidal_operation_impl {
    use super::*;
    impl<T: Clone + PartialEq, F: Fn(&T, &T) -> T> MonoidalOperation<T, F> {
        pub fn new(e: T, op: F) -> Self {
            Self { e, op }
        }
    }
    impl<T: Clone + PartialEq, F: Fn(&T, &T) -> T> Magma for MonoidalOperation<T, F> {
        type T = T;
        #[inline]
        fn operate(&self, x: &Self::T, y: &Self::T) -> Self::T {
            (self.op)(x, y)
        }
    }
    impl<T: Clone + PartialEq, F: Fn(&T, &T) -> T> Unital for MonoidalOperation<T, F> {
        #[inline]
        fn unit(&self) -> Self::T {
            self.e.clone()
        }
    }
    impl<T: Clone + PartialEq, F: Fn(&T, &T) -> T> Associative for MonoidalOperation<T, F> {}
    impl<T: Clone + PartialEq, F: Fn(&T, &T) -> T> Commutative for MonoidalOperation<T, F> {}
}
/// M: folding Monoid
/// E: lazy Monoid
/// F: lazy evaluating
#[derive(Clone, Debug)]
pub struct LazySegmentTree<M: Monoid, E: Monoid, F: Fn(&M::T, &E::T) -> M::T> {
    n: usize,
    height: usize,
    seg: Vec<M::T>,
    lazy: Vec<E::T>,
    m: M,
    e: E,
    f: F,
}
impl<M: Monoid, E: Monoid, F: Fn(&M::T, &E::T) -> M::T> LazySegmentTree<M, E, F> {
    pub fn new(n: usize, m: M, e: E, f: F) -> Self {
        let height = format!("{:b}", n - 1).len();
        let n = 1 << height;
        let seg = vec![m.unit(); 2 * n];
        let lazy = vec![e.unit(); 2 * n];
        Self {
            n,
            height,
            seg,
            lazy,
            m,
            e,
            f,
        }
    }
    pub fn from_vec(v: Vec<M::T>, m: M, e: E, f: F) -> Self {
        let height = format!("{:b}", v.len() - 1).len();
        let n = 1 << height;
        let mut seg = vec![m.unit(); 2 * n];
        for (i, x) in v.into_iter().enumerate() {
            seg[i + n] = x;
        }
        for i in (1..n).rev() {
            seg[i] = m.operate(&seg[2 * i], &seg[2 * i + 1]);
        }
        let lazy = vec![e.unit(); 2 * n];
        Self {
            n,
            height,
            seg,
            lazy,
            m,
            e,
            f,
        }
    }
    #[inline]
    fn propagate(&mut self, k: usize) {
        debug_assert!(k < self.n);
        if self.lazy[k] != self.e.unit() {
            self.lazy[2 * k] = self.e.operate(&self.lazy[2 * k], &self.lazy[k]);
            self.lazy[2 * k + 1] = self.e.operate(&self.lazy[2 * k + 1], &self.lazy[k]);
            self.seg[k] = self.reflect(k);
            self.lazy[k] = self.e.unit();
        }
    }
    #[inline]
    fn thrust(&mut self, k: usize) {
        for i in (1..=self.height).rev() {
            self.propagate(k >> i);
        }
    }
    #[inline]
    fn reflect(&self, k: usize) -> M::T {
        if self.lazy[k] != self.e.unit() {
            (self.f)(&self.seg[k], &self.lazy[k])
        } else {
            self.seg[k].clone()
        }
    }
    #[inline]
    fn recalc(&mut self, mut k: usize) {
        k /= 2;
        while k > 0 {
            self.seg[k] = self
                .m
                .operate(&self.reflect(2 * k), &self.reflect(2 * k + 1));
            k /= 2;
        }
    }
    pub fn update(&mut self, l: usize, r: usize, x: E::T) {
        debug_assert!(l < self.n);
        debug_assert!(r <= self.n);
        let mut a = l + self.n;
        let mut b = r + self.n;
        self.thrust(a);
        self.thrust(b - 1);
        while a < b {
            if a & 1 != 0 {
                self.lazy[a] = self.e.operate(&self.lazy[a], &x);
                a += 1;
            }
            if b & 1 != 0 {
                b -= 1;
                self.lazy[b] = self.e.operate(&self.lazy[b], &x);
            }
            a /= 2;
            b /= 2;
        }
        self.recalc(l + self.n);
        self.recalc(r + self.n - 1);
    }
    pub fn fold(&mut self, l: usize, r: usize) -> M::T {
        debug_assert!(l < self.n);
        debug_assert!(r <= self.n);
        let mut l = l + self.n;
        let mut r = r + self.n;
        self.thrust(l);
        self.thrust(r - 1);
        let mut vl = self.m.unit();
        let mut vr = self.m.unit();
        while l < r {
            if l & 1 != 0 {
                vl = self.m.operate(&vl, &self.reflect(l));
                l += 1;
            }
            if r & 1 != 0 {
                r -= 1;
                vr = self.m.operate(&self.reflect(r), &vr);
            }
            l /= 2;
            r /= 2;
        }
        self.m.operate(&vl, &vr)
    }
    pub fn set(&mut self, k: usize, x: M::T) {
        let k = k + self.n;
        self.thrust(k);
        self.seg[k] = x;
        self.lazy[k] = self.e.unit();
        self.recalc(k);
    }
    pub fn get(&mut self, k: usize) -> M::T {
        self.fold(k, k + 1)
    }
    pub fn fold_all(&mut self) -> M::T {
        self.fold(0, self.n)
    }
    pub fn as_slice(&self) -> &[M::T] {
        &self.seg[self.n..]
    }
    pub fn as_slice_lazy(&self) -> &[E::T] {
        &self.lazy[self.n..]
    }
}
/// retain the last element
#[derive(Clone, Copy, Debug, Default, Eq, Hash, Ord, PartialEq, PartialOrd)]
pub struct LastOperation<T: Clone + PartialEq> {
    _marker: std::marker::PhantomData<fn() -> T>,
}
mod last_operation_impl {
    use super::*;
    impl<T: Clone + PartialEq> LastOperation<T> {
        pub fn new() -> Self {
            Self {
                _marker: std::marker::PhantomData,
            }
        }
    }
    impl<T: Clone + PartialEq> Magma for LastOperation<T> {
        type T = Option<T>;
        #[inline]
        fn operate(&self, x: &Self::T, y: &Self::T) -> Self::T {
            y.as_ref().or(x.as_ref()).cloned()
        }
    }
    impl<T: Clone + PartialEq> Unital for LastOperation<T> {
        #[inline]
        fn unit(&self) -> Self::T {
            None
        }
    }
    impl<T: Clone + PartialEq> Associative for LastOperation<T> {}
    impl<T: Clone + PartialEq> Idempotent for LastOperation<T> {}
}
fn main() {
    #[allow(unused_imports)]
    use std::io::{Read as _, Write as _};
    let __out = std::io::stdout();
    let mut __in_buf = String::new();
    std::io::stdin().read_to_string(&mut __in_buf).unwrap();
    let mut scanner = Scanner::new(&__in_buf);
    #[allow(unused_macros)]
    macro_rules !scan {() =>{scan !(usize ) } ;(($($t :tt ) ,*) ) =>{($(scan !($t ) ) ,*) } ;([$t :tt ;$len :expr ] ) =>{(0 ..$len ) .map (|_ |scan !($t ) ) .collect ::<Vec <_ >>() } ;({chars :$b :expr } ) =>{scanner .scan_chars_with ($b ) } ;({$t :tt =>$f :expr } ) =>{$f (scan !($t ) ) } ;(chars ) =>{scanner .scan_chars () } ;($t :ty ) =>{scanner .scan ::<$t >() } ;}
    let mut __out = std::io::BufWriter::new(__out.lock());
    #[allow(unused_macros)]
    macro_rules !print {($($arg :tt ) *) =>(::std ::write !(__out ,$($arg ) *) .unwrap () ) }
    #[allow(unused_macros)]
    macro_rules !println {($($arg :tt ) *) =>(::std ::writeln !(__out ,$($arg ) *) .unwrap () ) }
    #[allow(unused_macros)]
    macro_rules! echo {
        ($iter :expr ) => {
            echo!($iter, "\n")
        };
        ($iter :expr ,$sep :expr ) => {
            let mut iter = $iter.into_iter();
            if let Some(item) = iter.next() {
                print!("{}", item);
            }
            for item in iter {
                print!("{}{}", $sep, item);
            }
            println!();
        };
    }
    let h = scan!();
    let w = scan!();
    let ab = scan!([(marker::Usize1, usize); h]);
    let v = (0..w).map(|i| (0, Some(i))).collect();
    let mut seg = LazySegmentTree::from_vec(
        v,
        MonoidalOperation::new((!0usize, None), |x, y| (x.0.min(y.0), x.1.max(y.1))),
        LastOperation::new(),
        |x, y| if let Some(y) = y { y } else { x }.clone(),
    );
    for (i, (a, b)) in ab.into_iter().enumerate() {
        let y = seg.fold(a, b).1;
        if b < w {
            let q = seg.get(b).1;
            if let Some(y) = y.max(q) {
                seg.set(b, (b - y, Some(y)));
            }
        }
        seg.update(a, b, Some((!0usize, None)));
        let ans = seg.fold_all().0.saturating_add(i + 1);
        println!("{}", if ans == !0 { -1 } else { ans as i64 });
    }
}