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 ;} } ;}
pub trait Modulus {
    fn get_modulus() -> u32;
    #[inline]
    fn modulo(x: u32) -> u32 {
        x % Self::get_modulus()
    }
}
#[allow(unused_macros)]
macro_rules! make_modulus {
    ($t :ident ,$e :expr ) => {
        pub struct $t {}
        impl Modulus for $t {
            #[inline]
            fn get_modulus() -> u32 {
                const MODULUS: u32 = $e;
                MODULUS
            }
        }
    };
}
#[allow(unused_macros)]
macro_rules! make_dynamic_modulus {
    ($t :ident ,$m :ident ,$e :expr ) => {
        pub struct $t {}
        static mut $m: u32 = $e;
        impl Modulus for $t {
            #[inline]
            fn get_modulus() -> u32 {
                unsafe { $m }
            }
        }
    };
}
pub mod modulus {
    use super::*;
    pub struct Modulo1000000007 {}
    impl Modulus for Modulo1000000007 {
        #[inline]
        fn get_modulus() -> u32 {
            const MODULUS: u32 = 1_000_000_007;
            MODULUS
        }
    }
    pub struct Modulo1000000009 {}
    impl Modulus for Modulo1000000009 {
        #[inline]
        fn get_modulus() -> u32 {
            const MODULUS: u32 = 1_000_000_009;
            MODULUS
        }
    }
    pub struct Modulo998244353 {}
    impl Modulus for Modulo998244353 {
        #[inline]
        fn get_modulus() -> u32 {
            const MODULUS: u32 = 998_244_353;
            MODULUS
        }
    }
    pub struct DynModulo {}
    static mut DYN_MODULUS: u32 = 1_000_000_007;
    impl Modulus for DynModulo {
        #[inline]
        fn get_modulus() -> u32 {
            unsafe { DYN_MODULUS }
        }
    }
    pub fn set_dyn_modulus(m: u32) {
        unsafe {
            DYN_MODULUS = m;
        }
    }
}
pub struct MInt<M>
where
    M: Modulus,
{
    x: u32,
    _marker: std::marker::PhantomData<fn() -> M>,
}
mod mint_impls {
    use super::*;
    use std::{
        cmp::Ordering,
        fmt::{self, Debug},
        hash::{Hash, Hasher},
        iter::{Product, Sum},
        marker::PhantomData,
        mem::swap,
        num::ParseIntError,
        ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Sub, SubAssign},
        str::FromStr,
    };
    impl<M: Modulus> MInt<M> {
        #[inline]
        pub fn new(x: u32) -> Self {
            Self {
                x: M::modulo(x),
                _marker: PhantomData,
            }
        }
        #[inline]
        pub fn new_unchecked(x: u32) -> Self {
            Self {
                x,
                _marker: PhantomData,
            }
        }
        #[inline]
        pub fn inner(self) -> u32 {
            self.x
        }
        #[inline]
        pub fn get_mod() -> u32 {
            M::get_modulus()
        }
        #[inline]
        pub fn pow(mut self, mut y: usize) -> Self {
            let mut x = Self::one();
            while y > 0 {
                if y & 1 == 1 {
                    x *= self;
                }
                self *= self;
                y >>= 1;
            }
            x
        }
        #[inline]
        /// only prime modulus
        pub fn inv(self) -> Self {
            let mut a = self.x;
            let (mut b, mut u, mut s) = (M::get_modulus(), 1, 0);
            let k = a.trailing_zeros();
            a >>= k;
            for _ in 0..k {
                if u & 1 == 1 {
                    u += M::get_modulus();
                }
                u /= 2;
            }
            while a != b {
                if b < a {
                    swap(&mut a, &mut b);
                    swap(&mut u, &mut s);
                }
                b -= a;
                if s < u {
                    s += M::get_modulus();
                }
                s -= u;
                let k = b.trailing_zeros();
                b >>= k;
                for _ in 0..k {
                    if s & 1 == 1 {
                        s += M::get_modulus();
                    }
                    s /= 2;
                }
            }
            Self::new_unchecked(s)
        }
    }
    impl<M: Modulus> Clone for MInt<M> {
        #[inline]
        fn clone(&self) -> Self {
            Self {
                x: Clone::clone(&self.x),
                _marker: PhantomData,
            }
        }
    }
    impl<M: Modulus> Copy for MInt<M> {}
    impl<M: Modulus> Debug for MInt<M> {
        fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
            Debug::fmt(&self.x, f)
        }
    }
    impl<M: Modulus> Default for MInt<M> {
        #[inline]
        fn default() -> Self {
            Self::zero()
        }
    }
    impl<M: Modulus> PartialEq for MInt<M> {
        #[inline]
        fn eq(&self, other: &Self) -> bool {
            PartialEq::eq(&self.x, &other.x)
        }
    }
    impl<M: Modulus> PartialOrd for MInt<M> {
        #[inline]
        fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
            PartialOrd::partial_cmp(&self.x, &other.x)
        }
    }
    impl<M: Modulus> Eq for MInt<M> {}
    impl<M: Modulus> Ord for MInt<M> {
        #[inline]
        fn cmp(&self, other: &Self) -> Ordering {
            Ord::cmp(&self.x, &other.x)
        }
    }
    impl<M: Modulus> Hash for MInt<M> {
        #[inline]
        fn hash<H: Hasher>(&self, state: &mut H) {
            Hash::hash(&self.x, state)
        }
    }
    impl<M: Modulus> From<u32> for MInt<M> {
        #[inline]
        fn from(x: u32) -> Self {
            Self::new(x)
        }
    }
    impl<M: Modulus> From<u64> for MInt<M> {
        #[inline]
        fn from(x: u64) -> Self {
            Self::new_unchecked((x % M::get_modulus() as u64) as u32)
        }
    }
    impl<M: Modulus> From<usize> for MInt<M> {
        #[inline]
        fn from(x: usize) -> Self {
            Self::new_unchecked((x % M::get_modulus() as usize) as u32)
        }
    }
    impl<M: Modulus> From<i32> for MInt<M> {
        #[inline]
        fn from(x: i32) -> Self {
            let x = x % M::get_modulus() as i32;
            if x < 0 {
                Self::new_unchecked((x + M::get_modulus() as i32) as u32)
            } else {
                Self::new_unchecked(x as u32)
            }
        }
    }
    impl<M: Modulus> From<i64> for MInt<M> {
        #[inline]
        fn from(x: i64) -> Self {
            let x = x % M::get_modulus() as i64;
            if x < 0 {
                Self::new_unchecked((x + M::get_modulus() as i64) as u32)
            } else {
                Self::new_unchecked(x as u32)
            }
        }
    }
    impl<M: Modulus> From<isize> for MInt<M> {
        #[inline]
        fn from(x: isize) -> Self {
            let x = x % M::get_modulus() as isize;
            if x < 0 {
                Self::new_unchecked((x + M::get_modulus() as isize) as u32)
            } else {
                Self::new_unchecked(x as u32)
            }
        }
    }
    impl<M: Modulus> Add for MInt<M> {
        type Output = Self;
        #[inline]
        fn add(self, rhs: Self) -> Self::Output {
            let mut x = self.x + rhs.x;
            if x >= M::get_modulus() {
                x -= M::get_modulus();
            }
            Self::new_unchecked(x)
        }
    }
    impl<M: Modulus> Sub for MInt<M> {
        type Output = Self;
        #[inline]
        fn sub(self, rhs: Self) -> Self::Output {
            if self.x < rhs.x {
                Self::new_unchecked(self.x + M::get_modulus() - rhs.x)
            } else {
                Self::new_unchecked(self.x - rhs.x)
            }
        }
    }
    impl<M: Modulus> Mul for MInt<M> {
        type Output = Self;
        #[inline]
        fn mul(self, rhs: Self) -> Self::Output {
            Self::new_unchecked((self.x as u64 * rhs.x as u64 % M::get_modulus() as u64) as u32)
        }
    }
    impl<M: Modulus> Div for MInt<M> {
        type Output = Self;
        #[inline]
        fn div(self, rhs: Self) -> Self::Output {
            self * rhs.inv()
        }
    }
    impl<M: Modulus> Neg for MInt<M> {
        type Output = Self;
        #[inline]
        fn neg(self) -> Self::Output {
            if self.x == 0 {
                Self::zero()
            } else {
                Self::new_unchecked(M::get_modulus() - self.x)
            }
        }
    }
    impl<M: Modulus> Sum for MInt<M> {
        #[inline]
        fn sum<I: Iterator<Item = Self>>(iter: I) -> Self {
            iter.fold(Self::zero(), Add::add)
        }
    }
    impl<M: Modulus> Product for MInt<M> {
        #[inline]
        fn product<I: Iterator<Item = Self>>(iter: I) -> Self {
            iter.fold(Self::one(), Mul::mul)
        }
    }
    impl<'a, M: Modulus + 'a> Sum<&'a MInt<M>> for MInt<M> {
        #[inline]
        fn sum<I: Iterator<Item = &'a Self>>(iter: I) -> Self {
            iter.fold(Self::zero(), Add::add)
        }
    }
    impl<'a, M: Modulus + 'a> Product<&'a MInt<M>> for MInt<M> {
        #[inline]
        fn product<I: Iterator<Item = &'a Self>>(iter: I) -> Self {
            iter.fold(Self::one(), Mul::mul)
        }
    }
    impl<M: Modulus> fmt::Display for MInt<M> {
        fn fmt<'a>(&self, f: &mut fmt::Formatter<'a>) -> Result<(), fmt::Error> {
            write!(f, "{}", self.x)
        }
    }
    impl<M: Modulus> FromStr for MInt<M> {
        type Err = ParseIntError;
        #[inline]
        fn from_str(s: &str) -> Result<Self, Self::Err> {
            s.parse::<u32>().map(Self::new)
        }
    }
    impl<M: Modulus> IterScan for MInt<M> {
        type Output = Self;
        #[inline]
        fn scan<'a, I: Iterator<Item = &'a str>>(iter: &mut I) -> Option<Self::Output> {
            iter.next()?.parse::<MInt<M>>().ok()
        }
    }
    impl<M: Modulus> Zero for MInt<M> {
        #[inline]
        fn zero() -> Self {
            Self::new_unchecked(0)
        }
    }
    impl<M: Modulus> One for MInt<M> {
        #[inline]
        fn one() -> Self {
            Self::new_unchecked(1)
        }
    }
    macro_rules! mint_ref_binop {
        ($imp :ident ,$method :ident ,$t :ty ) => {
            impl<M: Modulus> $imp<$t> for &$t {
                type Output = <$t as $imp<$t>>::Output;
                #[inline]
                fn $method(self, other: $t) -> <$t as $imp<$t>>::Output {
                    $imp::$method(*self, other)
                }
            }
            impl<M: Modulus> $imp<&$t> for $t {
                type Output = <$t as $imp<$t>>::Output;
                #[inline]
                fn $method(self, other: &$t) -> <$t as $imp<$t>>::Output {
                    $imp::$method(self, *other)
                }
            }
            impl<M: Modulus> $imp<&$t> for &$t {
                type Output = <$t as $imp<$t>>::Output;
                #[inline]
                fn $method(self, other: &$t) -> <$t as $imp<$t>>::Output {
                    $imp::$method(*self, *other)
                }
            }
        };
    }
    mint_ref_binop!(Add, add, MInt<M>);
    mint_ref_binop!(Sub, sub, MInt<M>);
    mint_ref_binop!(Mul, mul, MInt<M>);
    mint_ref_binop!(Div, div, MInt<M>);
    macro_rules! mint_ref_unop {
        ($imp :ident ,$method :ident ,$t :ty ) => {
            impl<M: Modulus> $imp for &$t {
                type Output = <$t as $imp>::Output;
                #[inline]
                fn $method(self) -> <$t as $imp>::Output {
                    $imp::$method(*self)
                }
            }
        };
    }
    mint_ref_unop!(Neg, neg, MInt<M>);
    macro_rules! mint_ref_op_assign {
        ($imp :ident ,$method :ident ,$t :ty ,$fromimp :ident ,$frommethod :ident ) => {
            impl<M: Modulus> $imp<$t> for $t {
                #[inline]
                fn $method(&mut self, rhs: $t) {
                    *self = $fromimp::$frommethod(*self, rhs);
                }
            }
            impl<M: Modulus> $imp<&$t> for $t {
                #[inline]
                fn $method(&mut self, other: &$t) {
                    $imp::$method(self, *other);
                }
            }
        };
    }
    mint_ref_op_assign!(AddAssign, add_assign, MInt<M>, Add, add);
    mint_ref_op_assign!(SubAssign, sub_assign, MInt<M>, Sub, sub);
    mint_ref_op_assign!(MulAssign, mul_assign, MInt<M>, Mul, mul);
    mint_ref_op_assign!(DivAssign, div_assign, MInt<M>, Div, div);
}
use std::ops::{Add, Div, Mul, Neg, Sub};
#[derive(Clone, Copy, Debug, Default, PartialEq, Eq, Hash)]
pub struct Complex<T> {
    pub re: T,
    pub im: T,
}
impl<T> Complex<T> {
    #[inline]
    pub fn new(re: T, im: T) -> Self {
        Complex { re, im }
    }
    #[inline]
    pub fn transpose(self) -> Self {
        Complex {
            re: self.im,
            im: self.re,
        }
    }
}
impl<T: Neg<Output = T>> Complex<T> {
    #[inline]
    pub fn conjugate(self) -> Self {
        Self::new(self.re, -self.im)
    }
}
impl<T: Add<Output = T> + Mul<Output = T>> Complex<T> {
    #[inline]
    pub fn dot(self, rhs: Self) -> T {
        self.re * rhs.re + self.im * rhs.im
    }
}
impl<T: Sub<Output = T> + Mul<Output = T>> Complex<T> {
    #[inline]
    pub fn cross(self, rhs: Self) -> T {
        self.re * rhs.im - self.im * rhs.re
    }
}
impl<T: Copy + Add<Output = T> + Mul<Output = T>> Complex<T> {
    #[inline]
    pub fn norm(self) -> T {
        self.re * self.re + self.im * self.im
    }
}
impl Complex<f64> {
    #[inline]
    pub fn polar(r: f64, theta: f64) -> Self {
        Self::new(r * theta.cos(), r * theta.sin())
    }
    #[inline]
    pub fn abs(self) -> f64 {
        self.re.hypot(self.im)
    }
    #[inline]
    pub fn unit(self) -> Self {
        self / self.abs()
    }
    #[inline]
    pub fn angle(self) -> f64 {
        self.im.atan2(self.re)
    }
}
impl<T: Add<Output = T>> Add for Complex<T> {
    type Output = Self;
    fn add(self, rhs: Self) -> Self::Output {
        Self::new(self.re + rhs.re, self.im + rhs.im)
    }
}
impl<T: Copy + Add<Output = T>> Add<T> for Complex<T> {
    type Output = Self;
    fn add(self, rhs: T) -> Self::Output {
        Self::new(self.re + rhs, self.im + rhs)
    }
}
impl<T: Sub<Output = T>> Sub for Complex<T> {
    type Output = Self;
    fn sub(self, rhs: Self) -> Self::Output {
        Self::new(self.re - rhs.re, self.im - rhs.im)
    }
}
impl<T: Copy + Sub<Output = T>> Sub<T> for Complex<T> {
    type Output = Self;
    fn sub(self, rhs: T) -> Self::Output {
        Self::new(self.re - rhs, self.im - rhs)
    }
}
impl<T: Copy + Add<Output = T> + Sub<Output = T> + Mul<Output = T>> Mul for Complex<T> {
    type Output = Self;
    fn mul(self, rhs: Self) -> Self::Output {
        Self::new(
            self.re * rhs.re - self.im * rhs.im,
            self.re * rhs.im + self.im * rhs.re,
        )
    }
}
impl<T: Copy + Mul<Output = T>> Mul<T> for Complex<T> {
    type Output = Self;
    fn mul(self, rhs: T) -> Self::Output {
        Self::new(self.re * rhs, self.im * rhs)
    }
}
impl<T: Copy + Add<Output = T> + Sub<Output = T> + Mul<Output = T> + Div<Output = T>> Div
    for Complex<T>
{
    type Output = Self;
    fn div(self, rhs: Self) -> Self::Output {
        let d = rhs.re * rhs.re + rhs.im * rhs.im;
        Self::new(
            (self.re * rhs.re + self.im * rhs.im) / d,
            (self.im * rhs.re - self.re * rhs.im) / d,
        )
    }
}
impl<T: Copy + Div<Output = T>> Div<T> for Complex<T> {
    type Output = Self;
    fn div(self, rhs: T) -> Self::Output {
        Self::new(self.re / rhs, self.im / rhs)
    }
}
impl<T: Neg<Output = T>> Neg for Complex<T> {
    type Output = Self;
    fn neg(self) -> Self::Output {
        Self::new(-self.re, -self.im)
    }
}
pub fn fast_fourier_transform(mut f: Vec<Complex<f64>>, inv: bool) -> Vec<Complex<f64>> {
    let n = f.len();
    debug_assert!(n.count_ones() == 1);
    let mask = n - 1;
    const TAU: f64 = 2. * std::f64::consts::PI;
    let omega = if inv { -TAU / n as f64 } else { TAU / n as f64 };
    let mut g = vec![Complex::<f64>::default(); n];
    let mut i = n / 2;
    while i >= 1 {
        let t = Complex::polar(1., omega * i as f64);
        let mut w = Complex::new(1., 0.);
        for j in (0..n).step_by(i) {
            for k in 0..i {
                g[j + k] = f[(j * 2 & mask) + k] + w * f[(j * 2 + i & mask) + k];
            }
            w = w * t;
        }
        i /= 2;
        std::mem::swap(&mut f, &mut g);
    }
    if inv {
        for a in f.iter_mut() {
            *a = *a / n as f64;
        }
    }
    f
}
pub fn convolve_i64(mut a: Vec<i64>, mut b: Vec<i64>) -> Vec<i64> {
    let m = a.len() + b.len() - 1;
    let n = 1usize << format!("{:b}", m).len();
    a.resize_with(n, Default::default);
    b.resize_with(n, Default::default);
    let a: Vec<_> = a.into_iter().map(|x| Complex::new(x as f64, 0.)).collect();
    let b: Vec<_> = b.into_iter().map(|x| Complex::new(x as f64, 0.)).collect();
    let mut a = fast_fourier_transform(a, false);
    for (a, b) in a.iter_mut().zip(fast_fourier_transform(b, false)) {
        *a = *a * b;
    }
    let c = fast_fourier_transform(a, true);
    c.into_iter().take(m).map(|x| x.re.round() as i64).collect()
}
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 n = scan!();
    let a = scan!([usize; n]);
    let mut ord = vec![0; P as usize];
    for i in 0..P as usize - 1 {
        ord[M::new(2).pow(i).inner() as usize] = i;
    }
    let mut ans = 0i64;
    let mut b = vec![0; P as usize];
    for a in a {
        ans -= M::from(a).pow(2).inner() as i64;
        if a > 0 {
            b[ord[a as usize]] += 1;
        }
    }
    let c = convolve_i64(b.clone(), b);
    for (i, c) in c.into_iter().enumerate() {
        ans += M::new_unchecked(2).pow(i).inner() as i64 * c as i64;
    }
    println!("{}", ans / 2);
}
const P: u32 = 200003;
make_modulus!(Mod, P);
type M = MInt<Mod>;

Measured memory_bytes: 31912