use std::collections::HashMap;
type Fp = fp::F1000000007;

fn main() {
    let mut buf = ngtio::with_stdin();
    let n = buf.usize();
    let a = buf.vec::<u32>(n);
    let sp = small_fp::SmallestPrimeFactors::new(a.iter().max().unwrap() + 1);
    let mut map = HashMap::new();
    a.iter()
        .map(|&x| sp.factorize(x))
        .enumerate()
        .map(|(i, div)| div.into_iter().map(move |(p, e)| (i, p, e)))
        .flatten()
        .for_each(|(i, p, e)| {
            let (first, ie) = map.entry(p).or_insert((0, None));
            if *first < e {
                *ie = Some((i, *first));
                *first = e;
            } else if *first == e {
                *ie = None;
            } else if let Some((_, second)) = ie {
                if *second < e {
                    *second = e;
                }
            }
        });
    let orig_cnt = map
        .iter()
        .map(|(&p, &(first, _))| Fp::new(p as i64).pow(first as u64))
        .product::<Fp>();
    let mut cnt = vec![orig_cnt; n];
    for (&p, &(first, ie)) in map.iter() {
        if let Some((i, e)) = ie {
            cnt[i] /= Fp::new(p as i64).pow((first - e) as u64);
        }
    }
    let mut b = std::iter::once(1)
        .chain(a.iter().copied())
        .map(|x| Fp::new(x as i64))
        .collect::<Vec<_>>();
    let mut c = std::iter::once(1)
        .chain(a.iter().rev().copied())
        .map(|x| Fp::new(x as i64))
        .collect::<Vec<_>>();
    accum::mul(&mut b);
    accum::mul(&mut c);
    for i in 0..n {
        let ans = b[i] * c[n - 1 - i] - cnt[i];
        println!("{}", ans);
    }
}

// dbg {{{
#[allow(dead_code)]
mod dbg {
    #[macro_export]
    macro_rules! lg {
        () => {
            $crate::eprintln!("[{}:{}]", $crate::file!(), $crate::line!());
        };
        ($val:expr) => {
            match $val {
                tmp => {
                    eprintln!("[{}:{}] {} = {:?}",
                        file!(), line!(), stringify!($val), &tmp);
                    tmp
                }
            }
        };
        ($val:expr,) => { $crate::lg!($val) };
        ($($val:expr),+ $(,)?) => {
            ($($crate::lg!($val)),+,)
        };
    }

    #[macro_export]
    macro_rules! lg_nl {
        () => {
            eprintln!("[{}:{}]", $crate::file!(), $crate::line!());
        };
        ($val:expr) => {
            match $val {
                tmp => {
                    eprintln!("[{}:{}] {}:\n{:?}", file!(), line!(), stringify!($val), tmp);
                    tmp
                }
            };
        };
    }

    #[macro_export]
    macro_rules! msg {
        () => {
            compile_error!();
        };
        ($msg:expr) => {
            $crate::eprintln!("[{}:{}][{}]", $crate::file!(), $crate::line!(), $msg);
        };
        ($msg:expr, $val:expr) => {
            match $val {
                tmp => {
                    eprintln!("[{}:{}][{}] {} = {:?}",
                        file!(), line!(), $msg, stringify!($val), &tmp);
                    tmp
                }
            }
        };
        ($msg:expr, $val:expr,) => { msg!($msg, $val) };
        ($msg:expr, $($val:expr),+ $(,)?) => {
            ($(msg!($msg, $val)),+,)
        };
    }

    #[macro_export]
    macro_rules! tabular {
        ($val:expr) => {
            $crate::lg_nl!($crate::Tabular($val))
        };
    }

    #[macro_export]
    macro_rules! boolean_table {
        ($val:expr) => {
            $crate::lg_nl!($crate::BooleanTable($val));
        };
    }

    #[macro_export]
    macro_rules! boolean_slice {
        ($val:expr) => {
            $crate::lg!($crate::BooleanSlice($val));
        };
    }

    use std::fmt::{Debug, Formatter};

    #[derive(Clone)]
    pub struct Tabular<'a, T: Debug>(pub &'a [T]);
    impl<'a, T: Debug> Debug for Tabular<'a, T> {
        fn fmt(&self, f: &mut Formatter) -> std::fmt::Result {
            for i in 0..self.0.len() {
                writeln!(f, "{:2} | {:?}", i, &self.0[i])?;
            }
            Ok(())
        }
    }

    #[derive(Clone)]
    pub struct BooleanTable<'a>(pub &'a [Vec<bool>]);
    impl<'a> Debug for BooleanTable<'a> {
        fn fmt(&self, f: &mut Formatter) -> std::fmt::Result {
            for i in 0..self.0.len() {
                writeln!(f, "{:2} | {:?}", i, BooleanSlice(&self.0[i]))?;
            }
            Ok(())
        }
    }

    #[derive(Clone)]
    pub struct BooleanSlice<'a>(pub &'a [bool]);
    impl<'a> Debug for BooleanSlice<'a> {
        fn fmt(&self, f: &mut Formatter) -> std::fmt::Result {
            write!(
                f,
                "{}",
                self.0
                    .iter()
                    .map(|&b| if b { "1 " } else { "0 " })
                    .collect::<String>()
            )?;
            Ok(())
        }
    }
}
// }}}
// small_fp {{{
#[allow(dead_code)]
mod small_fp {
    use crate::fp::{Fp, Mod};

    pub struct SmallInversions<T>(Vec<Fp<T>>);
    impl<T: Mod> SmallInversions<T> {
        pub fn new(n: u32) -> Self {
            let mut vec = vec![Fp::new(1); n as usize];
            for x in (2..n).map(|x| x as i64) {
                let q = Fp::<T>::r#mod() / x;
                let r = Fp::<T>::r#mod() % x;
                vec[x as usize] = -Fp::new(q) * vec[r as usize];
            }
            Self(vec)
        }
        pub fn inv_small(&self, n: u32) -> Fp<T> {
            self.0[n as usize]
        }
        pub fn inv_large(&self, n: i64) -> Fp<T> {
            if 0 <= n && n < self.0.len() as i64 {
                self.inv_small(n as u32)
            } else {
                let n = Fp::<T>::new(n).into_inner();
                let m = Fp::<T>::r#mod();
                let q = m / n;
                let r = m % n;
                -Fp::new(q) * self.inv_large(r)
            }
        }
    }

    pub struct SmallestPrimeFactors(Vec<u32>);
    impl SmallestPrimeFactors {
        pub fn new(n: u32) -> Self {
            let mut vec = (0..n).collect::<Vec<_>>();
            for p in (2..).take_while(|&p| p * p < n) {
                let mut i = 2 * p;
                while i < n {
                    if vec[i as usize] == i {
                        vec[i as usize] = p
                    }
                    i += p;
                }
            }
            Self(vec)
        }
        pub fn get(&self, n: u32) -> u32 {
            assert!(n != 0 && n < self.0.len() as u32);
            self.0[n as usize]
        }
        pub fn factorize(&self, mut n: u32) -> Vec<(u32, u32)> {
            let mut ans = Vec::new();
            while n != 1 {
                let p = self.0[n as usize];
                if ans.last().map_or(true, |&(p1, _)| p1 != p) {
                    ans.push((p, 0));
                }
                ans.last_mut().unwrap().1 += 1;
                n /= p;
            }
            ans
        }
    }
}
// }}}
// accum {{{
#[allow(dead_code)]
mod accum {
    use std::{
        cmp::Ord,
        ops::{
            AddAssign, BitAndAssign, BitOrAssign, BitXorAssign, DivAssign, MulAssign, SubAssign,
        },
    };
    pub fn add<T: Copy + AddAssign>(a: &mut [T]) {
        for_each_mut(a, |&mut x, y| *y += x);
    }
    pub fn add_inv<T: Copy + SubAssign>(a: &mut [T]) {
        rfor_each_mut(a, |&mut x, y| *y -= x);
    }
    pub fn mul<T: Copy + MulAssign>(a: &mut [T]) {
        for_each_mut(a, |&mut x, y| *y *= x);
    }
    pub fn mul_inv<T: Copy + DivAssign>(a: &mut [T]) {
        rfor_each_mut(a, |&mut x, y| *y /= x);
    }
    // -- ord
    pub fn min<T: Copy + Ord>(a: &mut [T]) {
        for_each_mut(a, |&mut x, y| *y = x.min(*y));
    }
    pub fn max<T: Copy + Ord>(a: &mut [T]) {
        for_each_mut(a, |&mut x, y| *y = x.max(*y));
    }
    // --  bit
    pub fn xor<T: Copy + BitXorAssign>(a: &mut [T]) {
        for_each_mut(a, |&mut x, y| *y ^= x);
    }
    pub fn xor_inv<T: Copy + BitXorAssign>(a: &mut [T]) {
        rfor_each_mut(a, |&mut x, y| *y ^= x);
    }
    pub fn or<T: Copy + BitOrAssign>(a: &mut [T]) {
        for_each_mut(a, |&mut x, y| *y |= x);
    }
    pub fn and<T: Copy + BitAndAssign>(a: &mut [T]) {
        for_each_mut(a, |&mut x, y| *y &= x);
    }
    // -- for_each
    pub fn for_each<T>(a: &[T], mut f: impl FnMut(&T, &T)) {
        if !a.is_empty() {
            for i in 1..a.len() {
                let (left, right) = a.split_at(i);
                f(left.last().unwrap(), right.first().unwrap());
            }
        }
    }
    pub fn rfor_each<T>(a: &[T], mut f: impl FnMut(&T, &T)) {
        if !a.is_empty() {
            for i in (1..a.len()).rev() {
                let (left, right) = a.split_at(i);
                f(left.last().unwrap(), right.first().unwrap());
            }
        }
    }
    pub fn for_each_mut<T>(a: &mut [T], mut f: impl FnMut(&mut T, &mut T)) {
        if !a.is_empty() {
            for i in 1..a.len() {
                let (left, right) = a.split_at_mut(i);
                f(left.last_mut().unwrap(), right.first_mut().unwrap());
            }
        }
    }
    pub fn rfor_each_mut<T>(a: &mut [T], mut f: impl FnMut(&mut T, &mut T)) {
        if !a.is_empty() {
            for i in (1..a.len()).rev() {
                let (left, right) = a.split_at_mut(i);
                f(left.last_mut().unwrap(), right.first_mut().unwrap());
            }
        }
    }
}
// }}}
// seq {{{
#[allow(dead_code)]
mod seq {
    #![warn(missing_docs, missing_doc_code_examples)]

    pub use self::accumulate::{accumulate, Accumulate};
    pub use self::adjacent::{adjacent, Adjacent};
    pub use self::cartesian_product::{cartesian_product, CartesianProduct};
    pub use self::format_intersparse::format_intersparse;
    pub use self::grid_next::{grid_next, GridNext};
    pub use self::intersperse::{intersperse, Intersperse};
    pub use self::mul_step::{mul_step, MulStep};
    pub use self::repeat_with::{repeat_with, RepeatWith};
    pub use self::step::{step, Step};

    use std::{fmt, ops};

    impl<I: Iterator> Seq for I {}

    pub trait Seq: Iterator + Sized {
        fn adjacent(self) -> Adjacent<Self, Self::Item>
        where
            Self::Item: Clone,
        {
            adjacent(self)
        }

        fn grid_next(self, ij: (usize, usize), h: usize, w: usize) -> GridNext<Self>
        where
            Self: Iterator<Item = (i64, i64)>,
        {
            grid_next(self, ij, h, w)
        }

        fn cartesian_product<J>(self, other: J) -> CartesianProduct<Self, J::IntoIter>
        where
            Self: Sized,
            Self::Item: Clone,
            J: IntoIterator,
            J::IntoIter: Clone,
        {
            cartesian_product::cartesian_product(self, other.into_iter())
        }

        fn accumulate<T>(self, init: T) -> Accumulate<Self, T>
        where
            T: Clone + ops::AddAssign<Self::Item>,
        {
            accumulate::accumulate(self, init)
        }

        fn intersperse(self, elt: Self::Item) -> Intersperse<Self> {
            intersperse::intersperse(self, elt)
        }

        fn format_intersparse<T>(self, separator: T) -> String
        where
            Self::Item: fmt::Display,
            T: fmt::Display,
        {
            self.map(|x| format!("{}", x))
                .intersperse(format!("{}", separator))
                .collect::<String>()
        }
    }

    mod adjacent {
        #[allow(missing_docs)]
        pub fn adjacent<I, T>(mut iter: I) -> Adjacent<I, T>
        where
            I: Iterator<Item = T>,
            T: Clone,
        {
            if let Some(first) = iter.next() {
                Adjacent {
                    iter,
                    prv: Some(first),
                }
            } else {
                Adjacent { iter, prv: None }
            }
        }

        #[allow(missing_docs)]
        pub struct Adjacent<I, T>
        where
            I: Iterator<Item = T>,
        {
            iter: I,
            prv: Option<T>,
        }

        impl<I, T> Iterator for Adjacent<I, T>
        where
            I: Iterator<Item = T>,
            T: Clone,
        {
            type Item = (T, T);

            fn next(&mut self) -> Option<(T, T)> {
                self.prv.as_ref().cloned().and_then(|first| {
                    self.iter.next().map(|second| {
                        self.prv = Some(second.clone());
                        (first, second)
                    })
                })
            }
        }
    }

    mod grid_next {
        #[allow(missing_docs)]
        pub fn grid_next<T>(difference: T, ij: (usize, usize), h: usize, w: usize) -> GridNext<T>
        where
            T: Iterator<Item = (i64, i64)>,
        {
            GridNext {
                i: ij.0 as i64,
                j: ij.1 as i64,
                h: h as i64,
                w: w as i64,
                difference,
            }
        }

        #[allow(missing_docs)]
        #[derive(Debug, Clone)]
        pub struct GridNext<T> {
            i: i64,
            j: i64,
            h: i64,
            w: i64,
            difference: T,
        }

        impl<T> Iterator for GridNext<T>
        where
            T: Iterator<Item = (i64, i64)>,
        {
            type Item = (usize, usize);

            fn next(&mut self) -> Option<(usize, usize)> {
                while let Some((di, dj)) = self.difference.next() {
                    let ni = self.i + di;
                    let nj = self.j + dj;
                    if 0 <= ni && ni < self.h && 0 <= nj && nj < self.w {
                        return Some((ni as usize, nj as usize));
                    }
                }
                None
            }
        }
    }

    mod step {
        #[allow(missing_docs)]
        pub fn step<T, U>(init: T, step: U) -> Step<T, U>
        where
            T: Copy,
            U: Copy,
            T: ::std::ops::Add<U, Output = T>,
        {
            Step { now: init, step }
        }

        #[allow(missing_docs)]
        #[derive(Debug, Clone)]
        pub struct Step<T, U> {
            now: T,
            step: U,
        }

        #[allow(missing_docs)]
        impl<T, U> Iterator for Step<T, U>
        where
            T: Copy,
            U: Copy,
            T: ::std::ops::Add<U, Output = T>,
        {
            type Item = T;

            fn next(&mut self) -> Option<T> {
                let next = self.now + self.step;
                Some(::std::mem::replace(&mut self.now, next))
            }
        }
    }

    mod mul_step {
        #[allow(missing_docs)]
        pub fn mul_step<T, U>(init: T, step: U) -> MulStep<T, U>
        where
            T: Copy,
            U: Copy,
            T: ::std::ops::Mul<U, Output = T>,
        {
            MulStep { now: init, step }
        }

        #[allow(missing_docs)]
        #[derive(Debug, Clone)]
        pub struct MulStep<T, U> {
            now: T,
            step: U,
        }

        #[allow(missing_docs)]
        impl<T, U> Iterator for MulStep<T, U>
        where
            T: Copy,
            U: Copy,
            T: ::std::ops::Mul<U, Output = T>,
        {
            type Item = T;

            fn next(&mut self) -> Option<T> {
                let next = self.now * self.step;
                Some(::std::mem::replace(&mut self.now, next))
            }
        }
    }

    mod repeat_with {
        #[allow(missing_docs)]
        pub fn repeat_with<A, F: FnMut() -> A>(repeater: F) -> RepeatWith<F> {
            RepeatWith { repeater }
        }

        #[allow(missing_docs)]
        #[derive(Debug, Clone)]
        pub struct RepeatWith<F> {
            repeater: F,
        }

        impl<A, F: FnMut() -> A> Iterator for RepeatWith<F> {
            type Item = A;

            #[inline]
            fn next(&mut self) -> Option<A> {
                Some((self.repeater)())
            }

            #[inline]
            fn size_hint(&self) -> (usize, Option<usize>) {
                (::std::usize::MAX, None)
            }
        }
    }

    mod accumulate {
        use super::*;

        #[allow(missing_docs)]
        #[derive(Debug, Clone)]
        pub struct Accumulate<I, T> {
            prev: Option<T>,
            iter: I,
        }

        #[allow(missing_docs)]
        pub fn accumulate<I, T>(iter: I, init: T) -> Accumulate<I, T>
        where
            I: Iterator,
            T: Clone + ops::AddAssign<I::Item>,
        {
            Accumulate {
                prev: Some(init),
                iter,
            }
        }

        impl<I, T> Iterator for Accumulate<I, T>
        where
            I: Iterator,
            T: Clone + ops::AddAssign<I::Item>,
        {
            type Item = T;

            fn next(&mut self) -> Option<T> {
                let res = self.prev.clone();
                if let Some(prev) = self.prev.as_mut() {
                    if let Some(next) = self.iter.next() {
                        *prev += next;
                    } else {
                        self.prev = None;
                    }
                }
                res
            }

            fn size_hint(&self) -> (usize, Option<usize>) {
                size_hint::add_scalar(self.iter.size_hint(), 1)
            }
        }
    }

    mod cartesian_product {
        #[allow(missing_docs)]
        #[derive(Debug, Clone)]
        pub struct CartesianProduct<I, J>
        where
            I: Iterator,
        {
            a: I,
            a_cur: Option<I::Item>,
            b: J,
            b_orig: J,
        }

        #[allow(missing_docs)]
        pub fn cartesian_product<I, J>(mut i: I, j: J) -> CartesianProduct<I, J>
        where
            I: Iterator,
            J: Clone + Iterator,
            I::Item: Clone,
        {
            CartesianProduct {
                a_cur: i.next(),
                a: i,
                b_orig: j.clone(),
                b: j,
            }
        }

        impl<I, J> Iterator for CartesianProduct<I, J>
        where
            I: Iterator,
            J: Clone + Iterator,
            I::Item: Clone,
        {
            type Item = (I::Item, J::Item);

            fn next(&mut self) -> Option<(I::Item, J::Item)> {
                let elt_b = match self.b.next() {
                    None => {
                        self.b = self.b_orig.clone();
                        match self.b.next() {
                            None => return None,
                            Some(x) => {
                                self.a_cur = self.a.next();
                                x
                            }
                        }
                    }
                    Some(x) => x,
                };
                match self.a_cur {
                    None => None,
                    Some(ref a) => Some((a.clone(), elt_b)),
                }
            }

            fn size_hint(&self) -> (usize, Option<usize>) {
                let has_cur = self.a_cur.is_some() as usize;
                // Not ExactSizeIterator because size may be larger than usize
                let (b_min, b_max) = self.b.size_hint();

                // Compute a * b_orig + b for both lower and upper bound
                super::size_hint::add(
                    super::size_hint::mul(self.a.size_hint(), self.b_orig.size_hint()),
                    (b_min * has_cur, b_max.map(move |x| x * has_cur)),
                )
            }

            fn fold<Acc, G>(mut self, mut accum: Acc, mut f: G) -> Acc
            where
                G: FnMut(Acc, Self::Item) -> Acc,
            {
                if let Some(mut a) = self.a_cur.take() {
                    let mut b = self.b;
                    loop {
                        accum = b.fold(accum, |acc, elt| f(acc, (a.clone(), elt)));

                        // we can only continue iterating a if we had a first element;
                        if let Some(next_a) = self.a.next() {
                            b = self.b_orig.clone();
                            a = next_a;
                        } else {
                            break;
                        }
                    }
                }
                accum
            }
        }
    }

    #[allow(missing_docs)]
    mod intersperse {
        use super::size_hint;
        use std::iter;

        #[derive(Debug, Clone)]
        #[must_use = "iterator adaptors are lazy and do nothing unless consumed"]
        pub struct Intersperse<I>
        where
            I: Iterator,
        {
            element: I::Item,
            iter: iter::Fuse<I>,
            peek: Option<I::Item>,
        }

        pub fn intersperse<I>(iter: I, elt: I::Item) -> Intersperse<I>
        where
            I: Iterator,
        {
            let mut iter = iter.fuse();
            Intersperse {
                peek: iter.next(),
                iter,
                element: elt,
            }
        }

        impl<I> Iterator for Intersperse<I>
        where
            I: Iterator,
            I::Item: Clone,
        {
            type Item = I::Item;
            #[inline]
            fn next(&mut self) -> Option<I::Item> {
                if self.peek.is_some() {
                    self.peek.take()
                } else {
                    self.peek = self.iter.next();
                    if self.peek.is_some() {
                        Some(self.element.clone())
                    } else {
                        None
                    }
                }
            }

            fn size_hint(&self) -> (usize, Option<usize>) {
                // 2 * SH + { 1 or 0 }
                let has_peek = self.peek.is_some() as usize;
                let sh = self.iter.size_hint();
                size_hint::add_scalar(size_hint::add(sh, sh), has_peek)
            }

            fn fold<B, F>(mut self, init: B, mut f: F) -> B
            where
                Self: Sized,
                F: FnMut(B, Self::Item) -> B,
            {
                let mut accum = init;

                if let Some(x) = self.peek.take() {
                    accum = f(accum, x);
                }

                let element = &self.element;

                self.iter.fold(accum, |accum, x| {
                    let accum = f(accum, element.clone());
                    f(accum, x)
                })
            }
        }
    }

    #[allow(missing_docs)]
    mod format_intersparse {
        use super::Seq;
        use std::fmt;

        pub fn format_intersparse<I, T>(iter: I, separator: T) -> String
        where
            I: Iterator,
            I::Item: fmt::Display,
            T: fmt::Display,
        {
            iter.map(|x| format!("{}", x))
                .intersperse(format!("{}", separator))
                .collect::<String>()
        }
    }

    mod size_hint {

        use std::cmp;
        use std::usize;

        pub type SizeHint = (usize, Option<usize>);

        #[inline]
        pub fn add(a: SizeHint, b: SizeHint) -> SizeHint {
            let min = a.0.saturating_add(b.0);
            let max = match (a.1, b.1) {
                (Some(x), Some(y)) => x.checked_add(y),
                _ => None,
            };

            (min, max)
        }

        #[inline]
        #[allow(dead_code)]
        pub fn add_scalar(sh: SizeHint, x: usize) -> SizeHint {
            let (mut low, mut hi) = sh;
            low = low.saturating_add(x);
            hi = hi.and_then(|elt| elt.checked_add(x));
            (low, hi)
        }

        #[inline]
        #[allow(dead_code)]
        pub fn sub_scalar(sh: SizeHint, x: usize) -> SizeHint {
            let (mut low, mut hi) = sh;
            low = low.saturating_sub(x);
            hi = hi.map(|elt| elt.saturating_sub(x));
            (low, hi)
        }

        #[inline]
        #[allow(dead_code)]
        pub fn mul(a: SizeHint, b: SizeHint) -> SizeHint {
            let low = a.0.saturating_mul(b.0);
            let hi = match (a.1, b.1) {
                (Some(x), Some(y)) => x.checked_mul(y),
                (Some(0), None) | (None, Some(0)) => Some(0),
                _ => None,
            };
            (low, hi)
        }

        #[inline]
        #[allow(dead_code)]
        pub fn mul_scalar(sh: SizeHint, x: usize) -> SizeHint {
            let (mut low, mut hi) = sh;
            low = low.saturating_mul(x);
            hi = hi.and_then(|elt| elt.checked_mul(x));
            (low, hi)
        }

        #[inline]
        #[allow(dead_code)]
        pub fn max(a: SizeHint, b: SizeHint) -> SizeHint {
            let (a_lower, a_upper) = a;
            let (b_lower, b_upper) = b;

            let lower = cmp::max(a_lower, b_lower);

            let upper = match (a_upper, b_upper) {
                (Some(x), Some(y)) => Some(cmp::max(x, y)),
                _ => None,
            };

            (lower, upper)
        }

        #[inline]
        #[allow(dead_code)]
        pub fn min(a: SizeHint, b: SizeHint) -> SizeHint {
            let (a_lower, a_upper) = a;
            let (b_lower, b_upper) = b;
            let lower = cmp::min(a_lower, b_lower);
            let upper = match (a_upper, b_upper) {
                (Some(u1), Some(u2)) => Some(cmp::min(u1, u2)),
                _ => a_upper.or(b_upper),
            };
            (lower, upper)
        }
    }
}
// }}}
// fp {{{
#[allow(dead_code)]
mod fp {
    mod arith {
        use super::{Fp, Mod};
        use std::ops::*;

        impl<T: Mod> Add for Fp<T> {
            type Output = Self;
            fn add(self, rhs: Self) -> Self {
                let res = self.0 + rhs.0;
                Self::unchecked(if T::MOD <= res { res - T::MOD } else { res })
            }
        }

        impl<T: Mod> Sub for Fp<T> {
            type Output = Self;
            fn sub(self, rhs: Self) -> Self {
                let res = self.0 - rhs.0;
                Self::unchecked(if res < 0 { res + T::MOD } else { res })
            }
        }

        impl<T: Mod> Mul for Fp<T> {
            type Output = Self;
            fn mul(self, rhs: Self) -> Self {
                Self::new(self.0 * rhs.0)
            }
        }

        #[allow(clippy::suspicious_arithmetic_impl)]
        impl<T: Mod> Div for Fp<T> {
            type Output = Self;
            fn div(self, rhs: Self) -> Self {
                self * rhs.inv()
            }
        }

        impl<M: Mod> Neg for Fp<M> {
            type Output = Self;
            fn neg(self) -> Self {
                if self.0 == 0 {
                    Self::unchecked(0)
                } else {
                    Self::unchecked(M::MOD - self.0)
                }
            }
        }

        impl<M: Mod> Neg for &Fp<M> {
            type Output = Fp<M>;
            fn neg(self) -> Self::Output {
                if self.0 == 0 {
                    Fp::unchecked(0)
                } else {
                    Fp::unchecked(M::MOD - self.0)
                }
            }
        }

        macro_rules! forward_assign_biop {
            ($(impl $trait:ident, $fn_assign:ident, $fn:ident)*) => {
                $(
                    impl<M: Mod> $trait for Fp<M> {
                        fn $fn_assign(&mut self, rhs: Self) {
                            *self = self.$fn(rhs);
                        }
                    }
                )*
            };
        }
        forward_assign_biop! {
            impl AddAssign, add_assign, add
            impl SubAssign, sub_assign, sub
            impl MulAssign, mul_assign, mul
            impl DivAssign, div_assign, div
        }

        macro_rules! forward_ref_binop {
            ($(impl $imp:ident, $method:ident)*) => {
                $(
                    impl<'a, T: Mod> $imp<Fp<T>> for &'a Fp<T> {
                        type Output = Fp<T>;
                        fn $method(self, other: Fp<T>) -> Self::Output {
                            $imp::$method(*self, other)
                        }
                    }

                    impl<'a, T: Mod> $imp<&'a Fp<T>> for Fp<T> {
                        type Output = Fp<T>;
                        fn $method(self, other: &Fp<T>) -> Self::Output {
                            $imp::$method(self, *other)
                        }
                    }

                    impl<'a, T: Mod> $imp<&'a Fp<T>> for &'a Fp<T> {
                        type Output = Fp<T>;
                        fn $method(self, other: &Fp<T>) -> Self::Output {
                            $imp::$method(*self, *other)
                        }
                    }
                )*
            };
        }
        forward_ref_binop! {
            impl Add, add
            impl Sub, sub
            impl Mul, mul
            impl Div, div
        }
    }

    use std::{
        fmt::{Debug, Display},
        hash::Hash,
        iter,
        marker::PhantomData,
        ops,
    };

    // NOTE: `crate::` がないとうまく展開できません。
    crate::define_fp!(pub F998244353, Mod998244353, 998244353);
    crate::define_fp!(pub F1000000007, Mod1000000007, 1000000007);

    #[derive(Clone, PartialEq, Copy, Eq, Hash)]
    pub struct Fp<T>(i64, PhantomData<T>);
    pub trait Mod: Debug + Clone + PartialEq + Copy + Eq + Hash {
        const MOD: i64;
    }
    impl<T: Mod> Fp<T> {
        pub fn new(mut x: i64) -> Self {
            x %= T::MOD;
            Self::unchecked(if x < 0 { x + T::MOD } else { x })
        }
        pub fn into_inner(self) -> i64 {
            self.0
        }
        pub fn r#mod() -> i64 {
            T::MOD
        }
        pub fn inv(self) -> Self {
            assert_ne!(self.0, 0, "Zero division");
            let (sign, x) = if self.0 * 2 < T::MOD {
                (1, self.0)
            } else {
                (-1, T::MOD - self.0)
            };
            let (g, _a, b) = ext_gcd(T::MOD, x);
            let ans = sign * b;
            assert_eq!(g, 1);
            Self::unchecked(if ans < 0 { ans + T::MOD } else { ans })
        }
        pub fn frac(x: i64, y: i64) -> Self {
            Fp::new(x) / Fp::new(y)
        }
        pub fn pow(mut self, mut p: u64) -> Self {
            let mut ans = Fp::new(1);
            while p != 0 {
                if p % 2 == 1 {
                    ans *= self;
                }
                self *= self;
                p /= 2;
            }
            ans
        }

        fn unchecked(x: i64) -> Self {
            Self(x, PhantomData)
        }
    }
    impl<T: Mod> iter::Sum<Fp<T>> for Fp<T> {
        fn sum<I>(iter: I) -> Self
        where
            I: iter::Iterator<Item = Fp<T>>,
        {
            iter.fold(Fp::new(0), ops::Add::add)
        }
    }

    impl<'a, T: 'a + Mod> iter::Sum<&'a Fp<T>> for Fp<T> {
        fn sum<I>(iter: I) -> Self
        where
            I: iter::Iterator<Item = &'a Fp<T>>,
        {
            iter.fold(Fp::new(0), ops::Add::add)
        }
    }

    impl<T: Mod> iter::Product<Fp<T>> for Fp<T> {
        fn product<I>(iter: I) -> Self
        where
            I: iter::Iterator<Item = Fp<T>>,
        {
            iter.fold(Self::new(1), ops::Mul::mul)
        }
    }

    impl<'a, T: 'a + Mod> iter::Product<&'a Fp<T>> for Fp<T> {
        fn product<I>(iter: I) -> Self
        where
            I: iter::Iterator<Item = &'a Fp<T>>,
        {
            iter.fold(Self::new(1), ops::Mul::mul)
        }
    }
    impl<T: Mod> Debug for Fp<T> {
        fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> Result<(), std::fmt::Error> {
            let (x, y, _z) = reduce(self.0, T::MOD);
            let (x, y) = match y.signum() {
                1 => (x, y),
                -1 => (-x, -y),
                _ => unreachable!(),
            };
            if y == 1 {
                write!(f, "{}", x)
            } else {
                write!(f, "{}/{}", x, y)
            }
        }
    }
    impl<T: Mod> Display for Fp<T> {
        fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> Result<(), std::fmt::Error> {
            write!(f, "{}", self.0)
        }
    }

    // ax + by = gcd(x, y) なる、互いに素な (a, b) を一組探して、(g, a, b) を返します。
    //
    // | 0  -x |   | y  -x | | x  0 |
    // | 1   b | = | a   b | | y  1 |
    fn ext_gcd(x: i64, y: i64) -> (i64, i64, i64) {
        let (b, g) = {
            let mut x = x;
            let mut y = y;
            let mut u = 0;
            let mut v = 1;
            while x != 0 {
                let q = y / x;
                y -= q * x;
                v -= q * u;
                std::mem::swap(&mut x, &mut y);
                std::mem::swap(&mut u, &mut v);
            }
            (v, y)
        };
        assert_eq!((g - b * y) % x, 0);
        let a = (g - b * y) / x;
        (g, a, b)
    }

    fn reduce(a: i64, m: i64) -> (i64, i64, i64) {
        if a.abs() < 10_000 {
            (a, 1, 0)
        } else {
            let mut q = m.div_euclid(a);
            let mut r = m.rem_euclid(a);
            if a <= 2 * r {
                q += 1;
                r -= a;
            }
            let (x, z, y) = reduce(r, a);
            (x, y - q * z, z)
        }
    }

    #[macro_export]
    macro_rules! define_fp {
        ($vis:vis $fp:ident, $t:ident, $mod:expr) => {
            #[derive(Debug, Clone, PartialEq, Copy, Eq, Hash)]
            $vis struct $t;
            // NOTE: `$crate::` があるとうまく展開できません。
            impl Mod for $t {
                const MOD: i64 = $mod;
            }
            // NOTE: `$crate::` があるとうまく展開できません。
            $vis type $fp = Fp<$t>;
        }
    }
}
// }}}
// ngtio {{{
#[allow(dead_code)]
mod ngtio {
    #![warn(missing_docs)]

    mod i {
        use std::{
            io::{self, BufRead},
            iter,
        };

        pub use self::multi_token::{Leaf, Parser, ParserTuple, RawTuple, Tuple, VecLen};
        pub use self::token::{Token, Usize1};

        pub fn with_stdin() -> Tokenizer<io::BufReader<io::Stdin>> {
            io::BufReader::new(io::stdin()).tokenizer()
        }

        pub fn with_str(src: &str) -> Tokenizer<&[u8]> {
            src.as_bytes().tokenizer()
        }

        pub struct Tokenizer<S: BufRead> {
            queue: Vec<String>, // FIXME: String のみにすると速そうです。
            scanner: S,
        }
        macro_rules! prim_method {
            ($name:ident: $T:ty) => {
#[allow(missing_docs)]
                pub fn $name(&mut self) -> $T {
                    <$T>::leaf().parse(self)
                }
            };
            ($name:ident) => {
                prim_method!($name: $name);
            };
        }
        macro_rules! prim_methods {
            ($name:ident: $T:ty; $($rest:tt)*) => {
                prim_method!($name:$T);
                prim_methods!($($rest)*);
            };
            ($name:ident; $($rest:tt)*) => {
                prim_method!($name);
                prim_methods!($($rest)*);
            };
            () => ()
        }
        impl<S: BufRead> Tokenizer<S> {
            pub fn token(&mut self) -> String {
                self.load();
                self.queue.pop().expect("入力が終了したのですが。")
            }
            pub fn new(scanner: S) -> Self {
                Self {
                    queue: Vec::new(),
                    scanner,
                }
            }
            fn load(&mut self) {
                while self.queue.is_empty() {
                    let mut s = String::new();
                    let length = self.scanner.read_line(&mut s).unwrap(); // 入力が UTF-8 でないときにエラーだそうです。
                    if length == 0 {
                        break;
                    }
                    self.queue = s.split_whitespace().rev().map(str::to_owned).collect();
                }
            }

            pub fn skip_line(&mut self) {
                assert!(
                    self.queue.is_empty(),
                    "行の途中で呼ばないでいただきたいです。現在のトークンキュー: {:?}",
                    &self.queue
                );
                self.load();
            }

            pub fn end(&mut self) {
                self.load();
                assert!(self.queue.is_empty(), "入力はまだあります！");
            }

            pub fn parse<T: Token>(&mut self) -> T::Output {
                T::parse(&self.token())
            }

            pub fn parse_collect<T: Token, B>(&mut self, n: usize) -> B
            where
                B: iter::FromIterator<T::Output>,
            {
                iter::repeat_with(|| self.parse::<T>()).take(n).collect()
            }

            pub fn tuple<T: RawTuple>(&mut self) -> <T::LeafTuple as Parser>::Output {
                T::leaf_tuple().parse(self)
            }

            pub fn vec<T: Token>(&mut self, len: usize) -> Vec<T::Output> {
                T::leaf().vec(len).parse(self)
            }

            pub fn vec_tuple<T: RawTuple>(
                &mut self,
                len: usize,
            ) -> Vec<<T::LeafTuple as Parser>::Output> {
                T::leaf_tuple().vec(len).parse(self)
            }

            pub fn vec2<T: Token>(&mut self, height: usize, width: usize) -> Vec<Vec<T::Output>> {
                T::leaf().vec(width).vec(height).parse(self)
            }

            pub fn vec2_tuple<T>(
                &mut self,
                height: usize,
                width: usize,
            ) -> Vec<Vec<<T::LeafTuple as Parser>::Output>>
            where
                T: RawTuple,
            {
                T::leaf_tuple().vec(width).vec(height).parse(self)
            }
            prim_methods! {
                u8; u16; u32; u64; u128; usize;
                i8; i16; i32; i64; i128; isize;
                char; string: String;
            }
        }

        mod token {
            use super::multi_token::Leaf;
            use std::{any, fmt, marker, str};

            pub trait Token: Sized {
                type Output;
                fn parse(s: &str) -> Self::Output;
                fn leaf() -> Leaf<Self> {
                    Leaf(marker::PhantomData)
                }
            }

            impl<T> Token for T
            where
                T: str::FromStr,
                <T as str::FromStr>::Err: fmt::Debug,
            {
                type Output = T;
                fn parse(s: &str) -> Self::Output {
                    s.parse().unwrap_or_else(|_| {
                        panic!("Parse error!: ({}: {})", s, any::type_name::<T>(),)
                    })
                }
            }

            pub struct Usize1 {}
            impl Token for Usize1 {
                type Output = usize;
                fn parse(s: &str) -> Self::Output {
                    usize::parse(s)
                        .checked_sub(1)
                        .expect("Parse error! (Zero substruction error of Usize1)")
                }
            }
        }

        mod multi_token {
            use super::{Token, Tokenizer};
            use std::{io::BufRead, iter, marker};

            pub trait Parser: Sized {
                type Output;
                fn parse<S: BufRead>(&self, server: &mut Tokenizer<S>) -> Self::Output;
                fn vec(self, len: usize) -> VecLen<Self> {
                    VecLen { len, elem: self }
                }
            }
            pub struct Leaf<T>(pub(super) marker::PhantomData<T>);
            impl<T: Token> Parser for Leaf<T> {
                type Output = T::Output;
                fn parse<S: BufRead>(&self, server: &mut Tokenizer<S>) -> T::Output {
                    server.parse::<T>()
                }
            }

            pub struct VecLen<T> {
                pub len: usize,
                pub elem: T,
            }
            impl<T: Parser> Parser for VecLen<T> {
                type Output = Vec<T::Output>;
                fn parse<S: BufRead>(&self, server: &mut Tokenizer<S>) -> Self::Output {
                    iter::repeat_with(|| self.elem.parse(server))
                        .take(self.len)
                        .collect()
                }
            }

            pub trait RawTuple {
                type LeafTuple: Parser;
                fn leaf_tuple() -> Self::LeafTuple;
            }
            pub trait ParserTuple {
                type Tuple: Parser;
                fn tuple(self) -> Self::Tuple;
            }
            pub struct Tuple<T>(pub T);
            macro_rules! impl_tuple {
                ($($t:ident: $T:ident),*) => {
                    impl<$($T),*> Parser for Tuple<($($T,)*)>
                        where
                            $($T: Parser,)*
                            {
                                type Output = ($($T::Output,)*);
#[allow(unused_variables)]
                                fn parse<S: BufRead >(&self, server: &mut Tokenizer<S>) -> Self::Output {
                                    match self {
                                        Tuple(($($t,)*)) => {
                                            ($($t.parse(server),)*)
                                        }
                                    }
                                }
                            }
                    impl<$($T: Token),*> RawTuple for ($($T,)*) {
                        type LeafTuple = Tuple<($(Leaf<$T>,)*)>;
                        fn leaf_tuple() -> Self::LeafTuple {
                            Tuple(($($T::leaf(),)*))
                        }
                    }
                    impl<$($T: Parser),*> ParserTuple for ($($T,)*) {
                        type Tuple = Tuple<($($T,)*)>;
                        fn tuple(self) -> Self::Tuple {
                            Tuple(self)
                        }
                    }
                };
            }
            impl_tuple!();
            impl_tuple!(t1: T1);
            impl_tuple!(t1: T1, t2: T2);
            impl_tuple!(t1: T1, t2: T2, t3: T3);
            impl_tuple!(t1: T1, t2: T2, t3: T3, t4: T4);
            impl_tuple!(t1: T1, t2: T2, t3: T3, t4: T4, t5: T5);
            impl_tuple!(t1: T1, t2: T2, t3: T3, t4: T4, t5: T5, t6: T6);
            impl_tuple!(t1: T1, t2: T2, t3: T3, t4: T4, t5: T5, t6: T6, t7: T7);
            impl_tuple!(
                t1: T1,
                t2: T2,
                t3: T3,
                t4: T4,
                t5: T5,
                t6: T6,
                t7: T7,
                t8: T8
            );
        }

        trait Scanner: BufRead + Sized {
            fn tokenizer(self) -> Tokenizer<Self> {
                Tokenizer::new(self)
            }
        }
        impl<R: BufRead> Scanner for R {}
    }

    pub use self::i::{with_stdin, with_str};

    pub mod prelude {
        pub use super::i::{Parser, ParserTuple, RawTuple, Token, Usize1};
    }
}
// }}}