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(Clone, Debug)]
pub struct Scanner<'a> {
    iter: std::str::SplitAsciiWhitespace<'a>,
}
mod scanner_impls {
    use super::*;
    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 as IterScan>::scan(&mut self.iter).expect("scan error")
        }
        #[inline]
        pub fn mscan<T: MarkedIterScan>(&mut self, marker: T) -> <T as MarkedIterScan>::Output {
            marker.mscan(&mut self.iter).expect("scan error")
        }
        #[inline]
        pub fn scan_vec<T: IterScan>(&mut self, size: usize) -> Vec<<T as IterScan>::Output> {
            (0..size)
                .map(|_| <T as IterScan>::scan(&mut self.iter).expect("scan error"))
                .collect()
        }
        #[inline]
        pub fn iter<'b, T: IterScan>(&'b mut self) -> ScannerIter<'a, 'b, T> {
            ScannerIter {
                inner: self,
                _marker: std::marker::PhantomData,
            }
        }
    }
    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 as IterScan >::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;
        #[inline]
        fn next(&mut self) -> Option<Self::Item> {
            <T as IterScan>::scan(&mut self.inner.iter)
        }
    }
}
pub mod marker {
    use super::*;
    use std::{iter::FromIterator, marker::PhantomData};
    #[derive(Debug, Copy, Clone)]
    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> {
            Some(<usize as IterScan>::scan(iter)?.checked_sub(1)?)
        }
    }
    #[derive(Debug, Copy, Clone)]
    pub struct Chars;
    impl IterScan for Chars {
        type Output = Vec<char>;
        #[inline]
        fn scan<'a, I: Iterator<Item = &'a str>>(iter: &mut I) -> Option<Self::Output> {
            Some(iter.next()?.chars().collect())
        }
    }
    #[derive(Debug, Copy, Clone)]
    pub struct CharsWithBase(char);
    impl MarkedIterScan for CharsWithBase {
        type Output = Vec<usize>;
        #[inline]
        fn mscan<'a, I: Iterator<Item = &'a str>>(self, iter: &mut I) -> Option<Self::Output> {
            Some(
                iter.next()?
                    .chars()
                    .map(|c| (c as u8 - self.0 as u8) as usize)
                    .collect(),
            )
        }
    }
    #[derive(Debug, Copy, Clone)]
    pub struct Collect<T: IterScan, B: FromIterator<<T as IterScan>::Output>> {
        size: usize,
        _marker: PhantomData<fn() -> (T, B)>,
    }
    impl<T: IterScan, B: FromIterator<<T as IterScan>::Output>> Collect<T, B> {
        pub fn new(size: usize) -> Self {
            Self {
                size,
                _marker: PhantomData,
            }
        }
    }
    impl<T: IterScan, B: FromIterator<<T as IterScan>::Output>> MarkedIterScan for Collect<T, B> {
        type Output = B;
        #[inline]
        fn mscan<'a, I: Iterator<Item = &'a str>>(self, iter: &mut I) -> Option<Self::Output> {
            Some(
                (0..self.size)
                    .map(|_| <T as IterScan>::scan(iter).expect("scan error"))
                    .collect::<B>(),
            )
        }
    }
}
#[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 {}
/// 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..]
    }
}
/// binary operation to select larger element
#[derive(Clone, Copy, Debug, Default, Eq, Hash, Ord, PartialEq, PartialOrd)]
pub struct MaxOperation<T: Clone + Ord + MinimumBounded> {
    _marker: std::marker::PhantomData<fn() -> T>,
}
pub trait MinimumBounded {
    fn minimum() -> Self;
}
mod max_operation_impl {
    use super::*;
    macro_rules! impl_minimum_with_min {
        ($t :ty ,$min :expr ) => {
            impl MinimumBounded for $t {
                #[inline]
                fn minimum() -> Self {
                    $min
                }
            }
        };
    }
    impl_minimum_with_min!(usize, std::usize::MIN);
    impl_minimum_with_min!(u8, std::u8::MIN);
    impl_minimum_with_min!(u16, std::u16::MIN);
    impl_minimum_with_min!(u32, std::u32::MIN);
    impl_minimum_with_min!(u64, std::u64::MIN);
    impl_minimum_with_min!(isize, std::isize::MIN);
    impl_minimum_with_min!(i8, std::i8::MIN);
    impl_minimum_with_min!(i16, std::i16::MIN);
    impl_minimum_with_min!(i32, std::i32::MIN);
    impl_minimum_with_min!(i64, std::i64::MIN);
    macro_rules !impl_minimum_tuple {($($T :ident ) *) =>{impl <$($T :MinimumBounded ) ,*>MinimumBounded for ($($T ,) *) {#[inline ] fn minimum () ->Self {($(<$T as MinimumBounded >::minimum () ,) *) } } } ;}
    impl_minimum_tuple!();
    impl_minimum_tuple!(A);
    impl_minimum_tuple !(A B ) ;
    impl_minimum_tuple !(A B C ) ;
    impl_minimum_tuple !(A B C D ) ;
    impl_minimum_tuple !(A B C D E ) ;
    impl_minimum_tuple !(A B C D E F ) ;
    impl_minimum_tuple !(A B C D E F G ) ;
    impl_minimum_tuple !(A B C D E F G H ) ;
    impl_minimum_tuple !(A B C D E F G H I ) ;
    impl_minimum_tuple !(A B C D E F G H I J ) ;
    impl_minimum_tuple !(A B C D E F G H I J K ) ;
    impl<T: Clone + Ord + MinimumBounded> MaxOperation<T> {
        pub fn new() -> Self {
            Self {
                _marker: std::marker::PhantomData,
            }
        }
    }
    impl<T: Clone + Ord + MinimumBounded> Magma for MaxOperation<T> {
        type T = T;
        #[inline]
        fn operate(&self, x: &Self::T, y: &Self::T) -> Self::T {
            x.max(y).clone()
        }
    }
    impl<T: Clone + Ord + MinimumBounded> Unital for MaxOperation<T> {
        #[inline]
        fn unit(&self) -> Self::T {
            MinimumBounded::minimum()
        }
    }
    impl<T: Clone + Ord + MinimumBounded> Associative for MaxOperation<T> {}
    impl<T: Clone + Ord + MinimumBounded> Commutative for MaxOperation<T> {}
    impl<T: Clone + Ord + MinimumBounded> Idempotent for MaxOperation<T> {}
}
/// binary operation to select smaller element
#[derive(Clone, Copy, Debug, Default, Eq, Hash, Ord, PartialEq, PartialOrd)]
pub struct MinOperation<T: Clone + Ord + MaximumBounded> {
    _marker: std::marker::PhantomData<fn() -> T>,
}
pub trait MaximumBounded {
    fn maximum() -> Self;
}
mod min_operation_impl {
    use super::*;
    macro_rules! impl_maximum_with_max {
        ($t :ty ,$max :expr ) => {
            impl MaximumBounded for $t {
                #[inline]
                fn maximum() -> Self {
                    $max
                }
            }
        };
    }
    impl_maximum_with_max!(usize, std::usize::MAX);
    impl_maximum_with_max!(u8, std::u8::MAX);
    impl_maximum_with_max!(u16, std::u16::MAX);
    impl_maximum_with_max!(u32, std::u32::MAX);
    impl_maximum_with_max!(u64, std::u64::MAX);
    impl_maximum_with_max!(isize, std::isize::MAX);
    impl_maximum_with_max!(i8, std::i8::MAX);
    impl_maximum_with_max!(i16, std::i16::MAX);
    impl_maximum_with_max!(i32, std::i32::MAX);
    impl_maximum_with_max!(i64, std::i64::MAX);
    macro_rules !impl_maximum_tuple {($($T :ident ) *) =>{impl <$($T :MaximumBounded ) ,*>MaximumBounded for ($($T ,) *) {#[inline ] fn maximum () ->Self {($(<$T as MaximumBounded >::maximum () ,) *) } } } ;}
    impl_maximum_tuple!();
    impl_maximum_tuple!(A);
    impl_maximum_tuple !(A B ) ;
    impl_maximum_tuple !(A B C ) ;
    impl_maximum_tuple !(A B C D ) ;
    impl_maximum_tuple !(A B C D E ) ;
    impl_maximum_tuple !(A B C D E F ) ;
    impl_maximum_tuple !(A B C D E F G ) ;
    impl_maximum_tuple !(A B C D E F G H ) ;
    impl_maximum_tuple !(A B C D E F G H I ) ;
    impl_maximum_tuple !(A B C D E F G H I J ) ;
    impl_maximum_tuple !(A B C D E F G H I J K ) ;
    impl<T: Clone + Ord + MaximumBounded> MinOperation<T> {
        pub fn new() -> Self {
            Self {
                _marker: std::marker::PhantomData,
            }
        }
    }
    impl<T: Clone + Ord + MaximumBounded> Magma for MinOperation<T> {
        type T = T;
        #[inline]
        fn operate(&self, x: &Self::T, y: &Self::T) -> Self::T {
            x.min(y).clone()
        }
    }
    impl<T: Clone + Ord + MaximumBounded> Unital for MinOperation<T> {
        #[inline]
        fn unit(&self) -> Self::T {
            MaximumBounded::maximum()
        }
    }
    impl<T: Clone + Ord + MaximumBounded> Associative for MinOperation<T> {}
    impl<T: Clone + Ord + MaximumBounded> Commutative for MinOperation<T> {}
    impl<T: Clone + Ord + MaximumBounded> Idempotent for MinOperation<T> {}
}
/// $(M_1, M_2)$
#[derive(Clone, Debug)]
pub struct CartesianOperation<M1, M2> {
    m1: M1,
    m2: M2,
}
mod cartesian_operation_impl {
    use super::*;
    impl<M1, M2> CartesianOperation<M1, M2> {
        pub fn new(m1: M1, m2: M2) -> Self {
            Self { m1, m2 }
        }
    }
    impl<M1: Magma, M2: Magma> Magma for CartesianOperation<M1, M2> {
        type T = (M1::T, M2::T);
        #[inline]
        fn operate(&self, x: &Self::T, y: &Self::T) -> Self::T {
            (self.m1.operate(&x.0, &y.0), self.m2.operate(&x.1, &y.1))
        }
    }
    impl<M1: Unital, M2: Unital> Unital for CartesianOperation<M1, M2> {
        #[inline]
        fn unit(&self) -> Self::T {
            (self.m1.unit(), self.m2.unit())
        }
    }
    impl<M1: Associative, M2: Associative> Associative for CartesianOperation<M1, M2> {}
    impl<M1: Commutative, M2: Commutative> Commutative for CartesianOperation<M1, M2> {}
    impl<M1: Invertible, M2: Invertible> Invertible for CartesianOperation<M1, M2> {
        #[inline]
        fn inverse(&self, x: &Self::T) -> Self::T {
            (self.m1.inverse(&x.0), self.m2.inverse(&x.1))
        }
    }
}
/// 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, unused_macros)]
    use std::io::{stdin, stdout, BufWriter, Read as _, Write as _};
    let mut _in_buf = Vec::new();
    stdin().read_to_end(&mut _in_buf).expect("io error");
    let _in_buf = unsafe { String::from_utf8_unchecked(_in_buf) };
    let mut scanner = Scanner::new(&_in_buf);
    macro_rules !scan {() =>{scan !(usize ) } ;(($($t :tt ) ,*) ) =>{($(scan !($t ) ) ,*) } ;([$t :ty ;$len :expr ] ) =>{scanner .scan_vec ::<$t >($len ) } ;([$t :tt ;$len :expr ] ) =>{(0 ..$len ) .map (|_ |scan !($t ) ) .collect ::<Vec <_ >>() } ;([$t :ty ] ) =>{scanner .iter ::<$t >() } ;({$e :expr } ) =>{scanner .mscan ($e ) } ;($t :ty ) =>{scanner .scan ::<$t >() } ;}
    let _out = stdout();
    let mut _out = BufWriter::new(_out.lock());
    macro_rules !print {($($arg :tt ) *) =>(::std ::write !(_out ,$($arg ) *) .expect ("io error" ) ) }
    macro_rules !println {($($arg :tt ) *) =>(::std ::writeln !(_out ,$($arg ) *) .expect ("io error" ) ) }
    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)]);
    let mut seg = LazySegmentTree::from_vec(
        (0..w).map(|i| (0usize, Some(i))).collect(),
        CartesianOperation::new(MinOperation::new(), MaxOperation::new()),
        LastOperation::new(),
        |&x, y| y.unwrap_or_else(|| x).clone(),
    );
    for (i, (a, b)) in ab.take(h).enumerate() {
        if b != w {
            if let Some(x) = seg.fold(0, b + 1).1 {
                seg.set(b, (b - x, Some(x)));
            }
        }
        seg.update(a, b, Some((!0usize, None)));
        let ans = seg.fold_all().0.saturating_add(i + 1);
        println!("{}", if ans == !0usize { -1 } else { ans as i64 });
    }
}
impl<T: Ord> MinimumBounded for Option<T> {
    #[inline]
    fn minimum() -> Self {
        None
    }
}

Measured memory_bytes: 29080