#![allow(non_snake_case)]
use crate::{fps::formal_power_series::fps_i64, scanner::Scanner};

fn main() {
    let mut scan = Scanner::new();
    let n = scan.int();
    let x = scan.int();
    if x > 200000 {
        println!("0");
        return;
    }
    let a = scan.readn::<isize>(n);
    let mut f = list![0;100001];
    for e in a {
        f[e] += 1;
    }
    let mut f = fps_i64(f);
    f.shrink();
    let f2 = &f * &f;
    println!("{}", f2[x]);
}
pub mod prime_number {

    use crate::arraylist::List;
    use crate::ext::int::IntExtra;

    pub struct MinFactor {
        pub is_prime: List<bool>,
        pub min_factor: List<isize>,
    }

    impl MinFactor {}

    pub fn primitive_root(m: i32) -> i32 {
        match m {
            2 => return 1,
            167_772_161 => return 3,
            469_762_049 => return 3,
            754_974_721 => return 11,
            998_244_353 => return 3,
            _ => {}
        }

        let mut divs = [0; 20];
        divs[0] = 2;
        let mut cnt = 1;
        let mut x = (m - 1) / 2;
        while x % 2 == 0 {
            x /= 2;
        }
        for i in (3..std::i32::MAX).step_by(2) {
            if i as i64 * i as i64 > x as i64 {
                break;
            }
            if x % i == 0 {
                divs[cnt] = i;
                cnt += 1;
                while x % i == 0 {
                    x /= i;
                }
            }
        }
        if x > 1 {
            divs[cnt] = x;
            cnt += 1;
        }
        let mut g = 2;
        loop {
            if (0..cnt).all(|i| g.pow_mod(((m - 1) / divs[i]) as i64, m) != 1) {
                break g as i32;
            }
            g += 1;
        }
    }
}
pub mod ext {
    pub mod range {
        use crate::independent::integer::Int;
        use std::cmp::{max, min};
        use std::ops::{Bound, Range, RangeBounds};

        pub trait IntRangeBounds<U: Int>: RangeBounds<U> {
            fn lbopt(&self) -> Option<U> {
                match self.start_bound() {
                    Bound::Included(x) => Some(*x),
                    Bound::Excluded(x) => Some(*x + U::one()),
                    Bound::Unbounded => None,
                }
            }

            fn ubopt(&self) -> Option<U> {
                match self.end_bound() {
                    Bound::Included(x) => Some(*x + U::one()),
                    Bound::Excluded(x) => Some(*x),
                    Bound::Unbounded => None,
                }
            }

            fn lower_bound(&self, limit: U) -> U {
                self.lbopt().map_or(limit, |x| max(limit, x))
            }

            fn upper_bound(&self, limit: U) -> U {
                self.ubopt().map_or(limit, |x| min(limit, x))
            }
            fn to_harfopen(&self, lb: U, ub: U) -> Range<U> {
                self.lower_bound(lb)..self.upper_bound(ub)
            }
            fn domain_of(&self, mut t: U) -> U {
                if let Some(x) = self.lbopt() {
                    if t < x {
                        t = x;
                    }
                }
                if let Some(x) = self.ubopt() {
                    if x <= t {
                        t = x - U::one();
                    }
                }
                t
            }
            fn width(&self) -> U {
                if self.empty() {
                    U::zero()
                } else {
                    self.ubopt().unwrap() - self.lbopt().unwrap()
                }
            }
            fn empty(&self) -> bool {
                match (self.lbopt(), self.ubopt()) {
                    (Some(lb), Some(ub)) => lb >= ub,
                    (None, _ub) => false,
                    (_lb, None) => false,
                }
            }
            fn contain_range(&self, inner: &Self) -> bool {
                (match (self.lbopt(), inner.lbopt()) {
                    (Some(a), Some(b)) => a <= b,
                    (None, _) => true,
                    (Some(_), None) => false,
                }) && (match (inner.ubopt(), self.ubopt()) {
                    (Some(a), Some(b)) => a <= b,
                    (_, None) => true,
                    (None, Some(_)) => false,
                })
            }
            fn separate_range(&self, other: &Self) -> bool {
                if let (Some(a), Some(b)) = (self.ubopt(), other.lbopt()) {
                    if a <= b {
                        return true;
                    }
                }
                if let (Some(a), Some(b)) = (other.ubopt(), self.lbopt()) {
                    if a <= b {
                        return true;
                    }
                }
                false
            }
            fn overlap(&self, other: &Self) -> Range<U> {
                let left = if let (Some(a), Some(b)) = (self.lbopt(), other.lbopt()) {
                    max(a, b)
                } else {
                    self.lbopt().or(other.lbopt()).unwrap()
                };
                let right = if let (Some(a), Some(b)) = (self.ubopt(), other.ubopt()) {
                    min(a, b)
                } else {
                    self.ubopt().or(other.ubopt()).unwrap()
                };
                left..right
            }
        }
        impl<T: ?Sized, U: Int> IntRangeBounds<U> for T where T: RangeBounds<U> {}
    }
    pub mod int {

        use crate::ext::range::IntRangeBounds;
        use crate::independent::integer::Int;
        use std::ops::RangeBounds;

        pub trait IntExtra: Int {
            fn chrange<U: RangeBounds<Self>>(self, range: U) -> Self {
                range.domain_of(self)
            }

            fn div_ceil(self, y: Self) -> Self {
                (self + y - Self::one()) / y
            }

            fn div_floor(self, y: Self) -> Self {
                self / y
            }

            fn ceil_multiple(self, y: Self) -> Self {
                self.div_ceil(y) * y
            }

            fn floor_multiple(self, y: Self) -> Self {
                self.div_floor(y) * y
            }
            fn pow_mod(mut self, mut n: i64, m: Self) -> Self {
                let mut res = Self::one();
                self %= m;
                while n > 0 {
                    if n & 1 == 1 {
                        res *= self;
                        res %= m;
                    }
                    self = (self * self) % m;
                    n >>= 1;
                }
                res
            }
        }

        impl<T> IntExtra for T where T: Int {}
    }
}
pub mod arraylist {

    use std::ops::*;
    use std::slice::Iter;

    use std::fmt::Formatter;
    use std::iter::FromIterator;

    #[derive(Clone, PartialEq, Eq, PartialOrd, Ord)]
    pub struct List<T> {
        pub data: Vec<T>,
    }

    impl<T> List<T> {
        #[inline]
        pub fn new() -> List<T> {
            List { data: vec![] }
        }
        #[inline]
        pub fn init(init: T, n: isize) -> List<T>
        where
            T: Clone,
        {
            List {
                data: vec![init; n as usize],
            }
        }

        #[inline]
        pub fn pop(&mut self) -> Option<T> {
            self.data.pop()
        }

        #[inline]
        pub fn reverse(&mut self) {
            self.data.reverse();
        }

        #[inline]
        pub fn append(&mut self, other: &lst<T>)
        where
            T: Clone,
        {
            self.data.append(&mut other.to_vec());
        }

        #[inline]
        pub fn resize(&mut self, new_len: isize, value: T)
        where
            T: Clone,
        {
            self.data.resize(new_len as usize, value);
        }
    }

    macro_rules! impl_idx {
        ($($tpe:ty, $t:ident [$($output:tt)+], $slf:ident, $index:ident, $f:expr),*) => {
            $(impl<$t> Index<$tpe> for List<$t> {
                type Output = $($output)+;
                #[inline]
                fn index(&$slf, $index: $tpe) -> &Self::Output {$f}
            })*
            $(impl<$t> Index<$tpe> for lst<$t> {
                type Output = $($output)+;
                #[inline]
                fn index(&$slf, $index: $tpe) -> &Self::Output {$f}
            })*
        }
    }

    macro_rules! impl_idx_mut {
        ($($tpe:ty, $slf:ident, $index:ident, $f:expr),*) => {
            $(impl<T> IndexMut<$tpe> for List<T> {
                #[inline]
                fn index_mut(&mut $slf, $index: $tpe) -> &mut Self::Output {$f}
            })*
            $(impl<T> IndexMut<$tpe> for lst<T> {
                #[inline]
                fn index_mut(&mut $slf, $index: $tpe) -> &mut Self::Output {$f}
            })*
        };
    }

    macro_rules! impl_idx_slice {
        ($($tpe:ty),*) => {
            impl_idx!($($tpe, T [lst<T>], self, i, self.as_slice(i)),*);
            impl_idx_mut!($($tpe, self, i, self.as_slice_mut(i)),*);
        };
    }

    impl_idx! {
        isize, T [T], self, i, self.at(i),
        char, T [T], self, i, self.at(i as isize - 'a' as isize)
    }

    impl_idx_slice! {
        Range<isize>, RangeTo<isize>, RangeFrom<isize>, RangeFull, RangeInclusive<isize>, RangeToInclusive<isize>
    }

    impl_idx_mut! {
        isize, self, i, self.at_mut(i),
        char, self, i, self.at_mut(i as isize - 'a' as isize)
    }

    impl<T> FromIterator<T> for List<T> {
        #[inline]
        fn from_iter<U: IntoIterator<Item = T>>(iter: U) -> Self {
            List {
                data: iter.into_iter().collect(),
            }
        }
    }

    impl<T> IntoIterator for List<T> {
        type Item = T;
        type IntoIter = std::vec::IntoIter<T>;

        #[inline]
        fn into_iter(self) -> std::vec::IntoIter<T> {
            self.data.into_iter()
        }
    }

    macro_rules! impl_traits {
        ($($tpe:tt),*) => {
            $(
                impl<T: std::fmt::Display> std::fmt::Display for $tpe<T> {
                    fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
                        write!(f, "{}", self.iter().map(|x| format!("{}", x)).collect::<Vec<_>>().join(" "))
                    }
                }

                impl<T: std::fmt::Debug> std::fmt::Debug for $tpe<T> {
                    fn fmt(&self, f: &mut Formatter<'_>) -> std::fmt::Result {
                        self.data.fmt(f)
                    }
                }

                impl<'a, T> IntoIterator for &'a $tpe<T> {
                    type Item = &'a T;
                    type IntoIter = Iter<'a, T>;

                    #[inline]
                    fn into_iter(self) -> Iter<'a, T> {
                        self.iter()
                    }
                }
            )*
        };
    }

    impl_traits!(List, lst);

    impl<T> From<Vec<T>> for List<T> {
        #[inline]
        fn from(vec: Vec<T>) -> Self {
            List { data: vec }
        }
    }

    impl<T: Clone> From<&[T]> for List<T> {
        #[inline]
        fn from(slice: &[T]) -> Self {
            slice.iter().cloned().collect()
        }
    }

    impl<T> Deref for List<T> {
        type Target = lst<T>;

        #[inline]
        fn deref(&self) -> &lst<T> {
            lst::new(&self.data)
        }
    }

    impl<T> DerefMut for List<T> {
        #[inline]
        fn deref_mut(&mut self) -> &mut lst<T> {
            lst::new_mut(&mut self.data)
        }
    }

    #[macro_export]
    macro_rules! list {
        () => { $crate::arraylist::List::new() };
        ($($v:expr),+ $(,)?) => { $crate::arraylist::List::from([$($v),+].to_vec()) };
        ($v:expr; $a:expr) => { $crate::arraylist::List::init($v, $a)};
        ($v:expr; $a:expr; $($rest:expr);+) => { $crate::arraylist::List::init(list!($v; $($rest);+), $a) };
    }

    #[allow(non_camel_case_types)]
    #[derive(PartialEq, Eq, PartialOrd, Ord)]
    #[repr(transparent)]
    pub struct lst<T> {
        data: [T],
    }

    impl<T> lst<T> {
        #[inline]
        pub fn new(slice: &[T]) -> &Self {
            unsafe { &*(slice as *const [T] as *const Self) }
        }
        #[inline]
        pub fn new_mut(slice: &mut [T]) -> &mut Self {
            unsafe { &mut *(slice as *mut [T] as *mut Self) }
        }
        #[inline]
        pub fn lens(&self) -> isize {
            self.data.len() as isize
        }
        #[inline]
        pub fn list(&self) -> List<T>
        where
            T: Clone,
        {
            self.cloned().collect()
        }

        #[inline]
        fn at(&self, index: isize) -> &T {
            if cfg!(debug_assertions) {
                self.data.index(index as usize)
            } else {
                unsafe { self.data.get_unchecked(index as usize) }
            }
        }
        #[inline]
        fn at_mut(&mut self, index: isize) -> &mut T {
            if cfg!(debug_assertions) {
                self.data.index_mut(index as usize)
            } else {
                unsafe { self.data.get_unchecked_mut(index as usize) }
            }
        }
        #[inline]
        pub fn as_slice(&self, range: impl RangeBounds<isize>) -> &lst<T> {
            if cfg!(debug_assertions) {
                lst::new(self.data.index(self.rgm(range)))
            } else {
                unsafe { lst::new(self.data.get_unchecked(self.rgm(range))) }
            }
        }
        #[inline]
        pub fn as_slice_mut(&mut self, range: impl RangeBounds<isize>) -> &mut lst<T> {
            if cfg!(debug_assertions) {
                lst::new_mut(self.data.index_mut(self.rgm(range)))
            } else {
                let r = self.rgm(range);
                unsafe { lst::new_mut(self.data.get_unchecked_mut(r)) }
            }
        }

        #[inline]
        pub fn cloned(&self) -> std::iter::Cloned<Iter<T>>
        where
            T: Clone,
        {
            self.iter().cloned()
        }

        #[inline]
        pub fn map<B, F>(&self, f: F) -> List<B>
        where
            T: Clone,
            F: FnMut(T) -> B,
        {
            self.cloned().map(f).collect()
        }

        #[inline]
        fn rgm(&self, r: impl RangeBounds<isize>) -> Range<usize> {
            (match r.start_bound() {
                Bound::Included(x) => *x as usize,
                Bound::Excluded(x) => *x as usize + 1,
                _ => 0,
            })
            .max(0)..(match r.end_bound() {
                Bound::Included(x) => *x as usize + 1,
                Bound::Excluded(x) => *x as usize,
                _ => self.len(),
            })
            .min(self.len())
        }
    }

    impl lst<isize> {}

    impl<T> Deref for lst<T> {
        type Target = [T];
        #[inline]
        fn deref(&self) -> &[T] {
            &self.data
        }
    }

    impl<T> DerefMut for lst<T> {
        #[inline]
        fn deref_mut(&mut self) -> &mut [T] {
            &mut self.data
        }
    }

    impl<'a, T> From<&'a [T]> for &'a lst<T> {
        #[inline]
        fn from(slice: &'a [T]) -> Self {
            lst::new(slice)
        }
    }
}
pub mod fps {
    pub mod convolution {
        use std::mem::swap;

        use crate::{
            arraylist::List,
            independent::integer::Int,
            modint,
            modulo::{ButterflyCache, ModInt, Modulus},
            prime_number::primitive_root,
        };

        fn prepare<M: Modulus>() -> ButterflyCache<M> {
            let g = ModInt::<M>::raw(primitive_root(M::M as i32) as u32);
            let mut es = [ModInt::<M>::raw(0); 30];
            let mut ies = [ModInt::<M>::raw(0); 30];
            let cnt2 = (M::M - 1).trailing_zeros() as usize;
            let mut e = g.pow((M::M - 1) >> cnt2);
            let mut ie = e.inv();
            for i in (2..=cnt2).rev() {
                es[i - 2] = e;
                ies[i - 2] = ie;
                e *= e;
                ie *= ie;
            }
            let sum_e = es
                .iter()
                .scan(ModInt::new(1), |acc, e| {
                    *acc *= *e;
                    Some(*acc)
                })
                .collect();
            let sum_ie = ies
                .iter()
                .scan(ModInt::new(1), |acc, ie| {
                    *acc *= *ie;
                    Some(*acc)
                })
                .collect();
            ButterflyCache { sum_e, sum_ie }
        }

        fn ceil_pow2(n: u32) -> u32 {
            32 - n.saturating_sub(1).leading_zeros()
        }

        fn inv_gcd(a: i64, b: i64) -> (i64, i64) {
            let a = a.rem_euclid(b);
            if a == 0 {
                return (b, 0);
            }

            let mut s = b;
            let mut t = a;
            let mut m0 = 0;
            let mut m1 = 1;

            while t != 0 {
                let u = s / t;
                s -= t * u;
                m0 -= m1 * u;

                swap(&mut s, &mut t);
                swap(&mut m0, &mut m1);
            }

            if m0 < 0 {
                m0 += b / s;
            }
            (s, m0)
        }

        fn butterfly<M: Modulus>(a: &mut [ModInt<M>]) {
            let n = a.len();
            let h = ceil_pow2(n as u32);

            M::butterfly_cache().with(|cache| {
                let mut cache = cache.borrow_mut();
                let ButterflyCache { sum_e, .. } = cache.get_or_insert_with(prepare);
                for ph in 1..=h {
                    let w = 1 << (ph - 1);
                    let p = 1 << (h - ph);
                    let mut now = ModInt::<M>::new(1);
                    for s in 0..w {
                        let offset = s << (h - ph + 1);
                        for i in 0..p {
                            let l = a[i + offset];
                            let r = a[i + offset + p] * now;
                            a[i + offset] = l + r;
                            a[i + offset + p] = l - r;
                        }
                        now *= sum_e[(!s).trailing_zeros() as usize];
                    }
                }
            });
        }

        fn butterfly_inv<M: Modulus>(a: &mut [ModInt<M>]) {
            let n = a.len();
            let h = ceil_pow2(n as u32);
            M::butterfly_cache().with(|cache| {
                let mut cache = cache.borrow_mut();
                let ButterflyCache { sum_ie, .. } = cache.get_or_insert_with(prepare);
                for ph in (1..=h).rev() {
                    let w = 1 << (ph - 1);
                    let p = 1 << (h - ph);
                    let mut inow = ModInt::<M>::new(1);
                    for s in 0..w {
                        let offset = s << (h - ph + 1);
                        for i in 0..p {
                            let l = a[i + offset];
                            let r = a[i + offset + p];
                            a[i + offset] = l + r;
                            a[i + offset + p] = ModInt::new(M::M + l.val - r.val) * inow;
                        }
                        inow *= sum_ie[(!s).trailing_zeros() as usize];
                    }
                }
            })
        }

        pub fn convolution_naive<T: Int>(a: &[T], b: &[T]) -> List<T> {
            if a.is_empty() || b.is_empty() {
                return vec![].into();
            }
            let (n, m) = (a.len(), b.len());
            let (n, m, a, b) = if n < m { (m, n, b, a) } else { (n, m, a, b) };
            let mut ans = vec![T::zero(); n + m - 1];
            for i in 0..n {
                for j in 0..m {
                    ans[i + j] += a[i] * b[j];
                }
            }
            ans.into()
        }

        pub fn convolution_ntt<M: Modulus>(a: &[ModInt<M>], b: &[ModInt<M>]) -> List<ModInt<M>> {
            if a.is_empty() || b.is_empty() {
                return vec![].into();
            }
            let (n, m) = (a.len(), b.len());

            if n.min(m) <= 60 {
                return convolution_naive(a, b);
            }

            let (mut a, mut b) = (a.to_owned(), b.to_owned());
            let z = 1 << ceil_pow2((n + m - 1) as _);
            a.resize(z, ModInt::raw(0));
            butterfly(&mut a);
            b.resize(z, ModInt::raw(0));
            butterfly(&mut b);
            for (a, b) in a.iter_mut().zip(&b) {
                *a *= *b;
            }
            butterfly_inv(&mut a);
            a.resize(n + m - 1, ModInt::raw(0));
            let iz = ModInt::new(z).inv();
            for a in &mut a {
                *a *= iz;
            }
            a.into()
        }

        pub fn convolution_raw<T: Int, M: Modulus>(a: &[T], b: &[T]) -> List<T> {
            let a = a.iter().cloned().map(ModInt::<M>::new).collect::<Vec<_>>();
            let b = b.iter().cloned().map(ModInt::<M>::new).collect::<Vec<_>>();
            convolution_ntt::<M>(&a, &b)
                .into_iter()
                .map(|z| T::from_u32(z.val))
                .collect()
        }

        pub fn convolution_i64(a: &[i64], b: &[i64]) -> List<i64> {
            const M1: u64 = 754_974_721;
            const M2: u64 = 167_772_161;
            const M3: u64 = 469_762_049;
            const M2M3: u64 = M2 * M3;
            const M1M3: u64 = M1 * M3;
            const M1M2: u64 = M1 * M2;
            const M1M2M3: u64 = M1M2.wrapping_mul(M3);

            modint!(M1);
            modint!(M2);
            modint!(M3);

            if a.is_empty() || b.is_empty() {
                return List::new();
            }

            let (_, i1) = inv_gcd(M2M3 as _, M1 as _);
            let (_, i2) = inv_gcd(M1M3 as _, M2 as _);
            let (_, i3) = inv_gcd(M1M2 as _, M3 as _);

            let c1 = convolution_raw::<_, M1>(a, b);
            let c2 = convolution_raw::<_, M2>(a, b);
            let c3 = convolution_raw::<_, M3>(a, b);

            c1.into_iter()
                .zip(c2)
                .zip(c3)
                .map(|((c1, c2), c3)| {
                    const OFFSET: &[u64] = &[0, 0, M1M2M3, 2 * M1M2M3, 3 * M1M2M3];

                    let mut x = [(c1, i1, M1, M2M3), (c2, i2, M2, M1M3), (c3, i3, M3, M1M2)]
                        .iter()
                        .map(|&(c, i, m1, m2)| {
                            c.wrapping_mul(i).rem_euclid(m1 as _).wrapping_mul(m2 as _)
                        })
                        .fold(0, i64::wrapping_add);

                    let mut diff = c1 - x.rem_euclid(M1 as _);
                    if diff < 0 {
                        diff += M1 as i64;
                    }
                    x = x.wrapping_sub(OFFSET[diff.rem_euclid(5) as usize] as _);
                    x
                })
                .collect()
        }
    }
    pub mod formal_power_series {
        use std::{
            fmt::Debug,
            marker::PhantomData,
            ops::{
                Add, AddAssign, Div, DivAssign, Index, IndexMut, Mul, MulAssign, Neg, Rem,
                RemAssign, Shl, Shr, Sub, SubAssign,
            },
        };

        use crate::{
            arraylist::{lst, List},
            independent::integer::Int,
            list,
            modulo::{ModInt, Modulus},
        };

        use crate::fps::convolution::{convolution_i64, convolution_naive, convolution_ntt};

        pub trait Convolution<T> {
            fn convolution(a: &[T], b: &[T]) -> List<T>;
        }

        #[derive(Debug, PartialEq, Eq, Copy, Clone, Hash, PartialOrd, Ord)]
        pub enum ConvolutionNTT {}
        impl<M: Modulus> Convolution<ModInt<M>> for ConvolutionNTT {
            fn convolution(a: &[ModInt<M>], b: &[ModInt<M>]) -> List<ModInt<M>> {
                convolution_ntt(a, b)
            }
        }

        #[derive(Debug, PartialEq, Eq, Copy, Clone, Hash, PartialOrd, Ord)]
        pub enum ConvolutionNaive {}
        impl<T: Int> Convolution<T> for ConvolutionNaive {
            fn convolution(a: &[T], b: &[T]) -> List<T> {
                convolution_naive(a, b)
            }
        }

        #[derive(Debug, PartialEq, Eq, Copy, Clone, Hash, PartialOrd, Ord)]
        pub enum ConvolutionI64 {}
        impl Convolution<i64> for ConvolutionI64 {
            fn convolution(a: &[i64], b: &[i64]) -> List<i64> {
                convolution_i64(a, b)
            }
        }

        impl<T: Int, F: Convolution<T>> From<&lst<T>> for FormalPowerSeries<T, F> {
            fn from(lst: &lst<T>) -> Self {
                Self::new(lst.list())
            }
        }

        #[derive(PartialEq, Eq)]
        pub struct FormalPowerSeries<T, F: Convolution<T>> {
            data: List<T>,
            phantom: PhantomData<fn() -> F>,
        }

        impl<T: Int, F: Convolution<T>> Clone for FormalPowerSeries<T, F> {
            fn clone(&self) -> Self {
                Self::new(self.data.clone())
            }
        }

        impl<T: Int + Debug, F: Convolution<T>> Debug for FormalPowerSeries<T, F> {
            fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
                self.data.fmt(f)
            }
        }

        impl<T: Int, F: Convolution<T>> FormalPowerSeries<T, F> {
            pub fn new(data: List<T>) -> FormalPowerSeries<T, F> {
                FormalPowerSeries {
                    data,
                    phantom: PhantomData,
                }
            }

            pub fn empty() -> Self {
                Self::new(List::new())
            }

            pub fn lens(&self) -> isize {
                self.data.lens()
            }

            pub fn is_empty(&self) -> bool {
                self.data.lens() == 0
            }

            pub fn resize(&mut self, new_len: isize) {
                self.data.resize(new_len, T::zero());
            }

            pub fn shrink(&mut self) {
                while self.data.last() == Some(&T::zero()) {
                    self.data.pop();
                }
            }

            pub fn pre(&self, size: isize) -> Self {
                Self::from(&self.data[..self.lens().min(size)])
            }

            pub fn rev(&self, deg: impl Into<Option<isize>>) -> Self {
                let deg = deg.into();
                let mut data = self.data.clone();
                if let Some(deg) = deg {
                    data.resize(deg, T::zero());
                }
                data.reverse();
                Self::new(data)
            }

            pub fn inv(&self, deg: impl Into<Option<isize>>) -> Self {
                assert!(self[0] != T::zero());
                let n = self.lens();
                let deg = deg.into().unwrap_or(n);
                let mut ret = Self::new(list![T::one() / self[0]]);
                let mut i = 1;
                while i < deg {
                    ret = (&ret + &ret - &ret * &ret * self.pre(i << 1)).pre(i << 1);
                    i <<= 1;
                }
                ret.pre(deg)
            }
        }

        macro_rules! impl_ops {
            ($tpe:ident, $fname:ident, $op:tt) => {
                impl<T: Int, F: Convolution<T>> $tpe<&Self> for FormalPowerSeries<T, F> {
                    type Output = FormalPowerSeries<T, F>;
                    fn $fname(self, rhs: &Self) -> Self::Output {
                        let mut ret: FormalPowerSeries<T, F> = self.clone();
                        ret $op rhs;
                        ret
                    }
                }
                impl<T: Int, F: Convolution<T>> $tpe for FormalPowerSeries<T, F> {
                    type Output = FormalPowerSeries<T, F>;
                    fn $fname(self, rhs: Self) -> Self::Output {
                        let mut ret: FormalPowerSeries<T, F> = self.clone();
                        ret $op &rhs;
                        ret
                    }
                }
                impl<T: Int, F: Convolution<T>> $tpe for &FormalPowerSeries<T, F> {
                    type Output = FormalPowerSeries<T, F>;
                    fn $fname(self, rhs: Self) -> Self::Output {
                        let mut ret: FormalPowerSeries<T, F> = self.clone();
                        ret $op rhs;
                        ret
                    }
                }
            };
        }

        impl_ops!(Add, add, +=);
        impl_ops!(Sub, sub, -=);
        impl_ops!(Mul, mul, *=);
        impl_ops!(Div, div, /=);
        impl_ops!(Rem, rem, %=);

        impl<T: Int, F: Convolution<T>> Neg for &FormalPowerSeries<T, F> {
            type Output = FormalPowerSeries<T, F>;

            fn neg(self) -> Self::Output {
                let data = self.data.map(|x| T::zero() - x);
                FormalPowerSeries {
                    data,
                    phantom: PhantomData,
                }
            }
        }

        impl<T: Int, F: Convolution<T>> AddAssign<&Self> for FormalPowerSeries<T, F> {
            fn add_assign(&mut self, rhs: &Self) {
                if rhs.lens() > self.lens() {
                    self.resize(rhs.lens())
                };
                self.data
                    .iter_mut()
                    .zip(rhs.data.iter())
                    .for_each(|(e, r)| *e += *r);
            }
        }

        impl<T: Int, F: Convolution<T>> AddAssign<T> for FormalPowerSeries<T, F> {
            fn add_assign(&mut self, rhs: T) {
                if self.is_empty() {
                    self.resize(1)
                };
                self[0] += rhs;
            }
        }

        impl<T: Int, F: Convolution<T>> SubAssign<&Self> for FormalPowerSeries<T, F> {
            fn sub_assign(&mut self, rhs: &Self) {
                if rhs.lens() > self.lens() {
                    self.resize(rhs.lens())
                };
                self.data
                    .iter_mut()
                    .zip(rhs.data.iter())
                    .for_each(|(e, r)| *e -= *r);
                self.shrink();
            }
        }

        impl<T: Int, F: Convolution<T>> SubAssign<T> for FormalPowerSeries<T, F> {
            fn sub_assign(&mut self, rhs: T) {
                if self.is_empty() {
                    self.resize(1);
                }
                self[0] -= rhs;
                self.shrink();
            }
        }

        impl<T: Int, F: Convolution<T>> MulAssign<T> for FormalPowerSeries<T, F> {
            fn mul_assign(&mut self, rhs: T) {
                for e in self.data.iter_mut() {
                    *e *= rhs;
                }
            }
        }

        impl<T: Int, F: Convolution<T>> MulAssign<&Self> for FormalPowerSeries<T, F> {
            fn mul_assign(&mut self, rhs: &Self) {
                if self.is_empty() || rhs.is_empty() {
                    self.data.data.clear();
                    return;
                }
                self.data = F::convolution(&self.data, &rhs.data);
            }
        }

        impl<T: Int, F: Convolution<T>> RemAssign<&Self> for FormalPowerSeries<T, F> {
            fn rem_assign(&mut self, rhs: &Self) {
                *self -= &(&*self / rhs * rhs);
            }
        }

        impl<T: Int, F: Convolution<T>> DivAssign<&Self> for FormalPowerSeries<T, F> {
            fn div_assign(&mut self, rhs: &Self) {
                if self.lens() < rhs.lens() {
                    self.data.data.clear();
                    return;
                }
                let n = self.lens() - rhs.lens() + 1;
                *self = (self.rev(None).pre(n) * rhs.rev(None).inv(n)).pre(n).rev(n);
            }
        }

        impl<T: Int, F: Convolution<T>> Shr<isize> for &FormalPowerSeries<T, F> {
            type Output = FormalPowerSeries<T, F>;

            fn shr(self, rhs: isize) -> Self::Output {
                if self.lens() <= rhs {
                    return FormalPowerSeries::<T, F>::empty();
                }
                Self::Output::from(&self.data[rhs..])
            }
        }

        impl<T: Int, F: Convolution<T>> Shl<isize> for &FormalPowerSeries<T, F> {
            type Output = FormalPowerSeries<T, F>;

            fn shl(self, rhs: isize) -> Self::Output {
                let mut data = list![T::zero();rhs];
                data.append(&self.data);
                Self::Output::new(data)
            }
        }

        impl<T: Int, F: Convolution<T>> Index<isize> for FormalPowerSeries<T, F> {
            type Output = T;

            fn index(&self, index: isize) -> &T {
                &self.data[index]
            }
        }

        impl<T: Int, F: Convolution<T>> IndexMut<isize> for FormalPowerSeries<T, F> {
            fn index_mut(&mut self, index: isize) -> &mut T {
                &mut self.data[index]
            }
        }

        pub fn fps_i64<T: Int>(lst: List<T>) -> FormalPowerSeries<T, ConvolutionI64>
        where
            ConvolutionI64: Convolution<T>,
        {
            FormalPowerSeries::new(lst)
        }

        #[macro_export]
        macro_rules! fps_ntt {
            () => {fps!(ConvolutionNTT)};
            ($($v:expr),+ $(,)?) => {fps!($($v),+;ConvolutionNTT)};
        }

        #[macro_export]
        macro_rules! fps_i64 {
            () => {fps!(ConvolutionI64)};
            ($($v:expr),+ $(,)?) => {fps!($($v),+;ConvolutionI64)};
        }

        #[macro_export]
        macro_rules! fps {
            ($tpe:ident) => { $crate::fps::formal_power_series::FormalPowerSeries::<_, $crate::fps::formal_power_series::$tpe>::empty() };
            ($($v:expr),+ $(,)?;$tpe:ident) => { $crate::fps::formal_power_series::FormalPowerSeries::<_, $crate::fps::formal_power_series::$tpe>::new(List::from([$($v),+].to_vec())) };
        }
    }
}

pub mod modulo {
    use crate::{impl_integer_functions, independent::integer::Int};
    use std::cell::RefCell;
    use std::fmt::Debug;
    use std::marker::PhantomData;
    use std::ops::*;
    use std::thread::LocalKey;

    #[derive(PartialEq, Eq, Copy, Clone, Hash, PartialOrd, Ord)]
    #[repr(transparent)]
    pub struct ModInt<T> {
        pub val: u32,
        phantom: PhantomData<fn() -> T>,
    }

    impl<T: Modulus> Debug for ModInt<T> {
        fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
            self.val.fmt(f)
        }
    }

    impl<T: Modulus> ModInt<T> {
        #[inline]
        pub fn new<U: Int>(a: U) -> Self {
            let x = a.to_i128();
            ModInt::raw(x.rem_euclid(T::M as i128) as _)
        }
        #[inline]
        pub fn pow<U: Int>(self, x: U) -> Self {
            let mut n = x.to_i64();
            let mut a = self;
            let mut res = Self::raw(1);
            while n > 0 {
                if n & 1 == 1 {
                    res *= a;
                }
                a = a * a;
                n >>= 1;
            }
            res
        }
        #[inline]
        pub fn inv(self) -> Self {
            self.pow(T::M - 2)
        }
        #[inline]
        pub fn raw(val: u32) -> Self {
            ModInt {
                val,
                phantom: PhantomData,
            }
        }
        #[inline]
        fn add_impl(self, other: Self) -> Self {
            let mut ret = self.val + other.val;
            if ret >= T::M {
                ret -= T::M;
            }
            Self::raw(ret)
        }
        #[inline]
        fn sub_impl(self, other: Self) -> Self {
            let mut ret = self.val.wrapping_sub(other.val);
            if ret >= T::M {
                ret = ret.wrapping_add(T::M);
            }
            Self::raw(ret)
        }
        #[inline]
        fn mul_impl(self, other: Self) -> Self {
            Self::raw((u64::from(self.val) * u64::from(other.val) % u64::from(T::M)) as _)
        }
        #[inline]
        fn div_impl(self, other: Self) -> Self {
            self * other.inv()
        }
        #[inline]
        fn rem_impl(self, other: Self) -> Self {
            Self::raw(self.val % other.val)
        }
    }

    pub trait Modulus: 'static + PartialEq + Eq + Copy + Clone + std::hash::Hash + Ord {
        const M: u32;
        fn butterfly_cache() -> &'static LocalKey<RefCell<Option<ButterflyCache<Self>>>>;
    }

    impl<T> std::fmt::Display for ModInt<T> {
        fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
            write!(f, "{}", self.val)
        }
    }

    macro_rules! impl_from_for_modint {
        ($($tpe:ident),*) => {
            $(
                impl<T: Modulus> From<$tpe> for ModInt<T> {
                    fn from(n: $tpe) -> Self {
                        Self::new(n)
                    }
                }
            )*
        };
    }

    impl_from_for_modint!(u8, u16, u32, u64, u128, i8, i16, i32, i64, i128, usize, isize);

    macro_rules! impl_assign {
        ($t1:ty, $t2:ty, $fa:ident, $f:ident, $f_impl:ident) => {
            impl<T: Modulus> $t1 for ModInt<T> {
                type Output = Self;
                #[inline]
                fn $f(self, other: Self) -> Self {
                    Self::$f_impl(self, other)
                }
            }
            impl<T: Modulus> $t2 for ModInt<T> {
                #[inline]
                fn $fa(&mut self, other: Self) {
                    *self = self.$f(other);
                }
            }
        };
    }

    impl_assign!(Add, AddAssign, add_assign, add, add_impl);
    impl_assign!(Sub, SubAssign, sub_assign, sub, sub_impl);
    impl_assign!(Mul, MulAssign, mul_assign, mul, mul_impl);
    impl_assign!(Div, DivAssign, div_assign, div, div_impl);
    impl_assign!(Rem, RemAssign, rem_assign, rem, rem_impl);

    #[macro_export]
    macro_rules! modint {
        () => {
            $crate::modint!(1000000007);
        };
        ($m:literal) => {
            $crate::modint!($m, ModValue);
            #[allow(dead_code)]
            type Z = $crate::modulo::ModInt<ModValue>;
        };
        ($name:ident) => {
            $crate::modint!($name, $name);
        };
        ($value:expr, $name:ident) => {
            #[derive(Debug, PartialEq, Eq, Copy, Clone, Hash, PartialOrd, Ord)]
            pub enum $name {}
            impl $crate::modulo::Modulus for $name {
                const M: u32 = $value as _;
                fn butterfly_cache() -> &'static ::std::thread::LocalKey<::std::cell::RefCell<::std::option::Option<$crate::modulo::ButterflyCache<Self>>>> {
                    thread_local! {
                        static BUTTERFLY_CACHE: ::std::cell::RefCell<::std::option::Option<$crate::modulo::ButterflyCache<$name>>> = ::std::default::Default::default();
                    }
                    &BUTTERFLY_CACHE
                }
            }
        };
    }

    impl<T: Modulus> Int for ModInt<T> {
        impl_integer_functions!(|s: &Self| s.val, |x| Self::new(x));
    }

    pub struct ButterflyCache<T> {
        pub sum_e: Vec<ModInt<T>>,
        pub sum_ie: Vec<ModInt<T>>,
    }
}
pub mod independent {
    pub mod integer {
        use std::fmt::Display;
        use std::ops::*;

        pub trait Int:
            Add<Output = Self>
            + Sub<Output = Self>
            + Mul<Output = Self>
            + Div<Output = Self>
            + Rem<Output = Self>
            + AddAssign
            + SubAssign
            + MulAssign
            + DivAssign
            + RemAssign
            + std::hash::Hash
            + PartialEq
            + Eq
            + PartialOrd
            + Ord
            + Copy
            + Display
        {
            fn to_u8(&self) -> u8;
            fn to_u16(&self) -> u16;
            fn to_u32(&self) -> u32;
            fn to_u64(&self) -> u64;
            fn to_u128(&self) -> u128;
            fn to_i8(&self) -> i8;
            fn to_i16(&self) -> i16;
            fn to_i32(&self) -> i32;
            fn to_i64(&self) -> i64;
            fn to_i128(&self) -> i128;
            fn to_usize(&self) -> usize;
            fn to_isize(&self) -> isize;
            fn from_u8(x: u8) -> Self;
            fn from_u16(x: u16) -> Self;
            fn from_u32(x: u32) -> Self;
            fn from_u64(x: u64) -> Self;
            fn from_u128(x: u128) -> Self;
            fn from_i8(x: i8) -> Self;
            fn from_i16(x: i16) -> Self;
            fn from_i32(x: i32) -> Self;
            fn from_i64(x: i64) -> Self;
            fn from_i128(x: i128) -> Self;
            fn from_usize(x: usize) -> Self;
            fn from_isize(x: isize) -> Self;
            fn zero() -> Self;
            fn one() -> Self;
            fn next(&self) -> Self {
                *self + Self::one()
            }
        }

        #[macro_export]
        macro_rules! impl_integer_functions {
            ($to_op:expr, $from_op:expr) => {
                impl_integer_functions!(
                    $to_op, $from_op,
                    to_u8, from_u8, u8,
                    to_u16, from_u16, u16,
                    to_u32, from_u32, u32,
                    to_u64, from_u64, u64,
                    to_u128, from_u128, u128,
                    to_i8, from_i8, i8,
                    to_i16, from_i16, i16,
                    to_i32, from_i32, i32,
                    to_i64, from_i64, i64,
                    to_i128, from_i128, i128,
                    to_usize, from_usize, usize,
                    to_isize, from_isize, isize
                );
            };
            ($to_op:expr, $from_op:expr, $($tofn:ident, $fromfn:ident, $tpe:ident),*) => {
                $(
                    fn $tofn(&self) -> $tpe {
                        $to_op(self) as $tpe
                    }
                    fn $fromfn(x: $tpe) -> Self {
                        $from_op(x)
                    }
                )*
                fn zero() -> Self {$from_op(0)}
                fn one() -> Self {$from_op(1)}
            };
        }

        macro_rules! impl_integer {
            ($($tpe:ident),*) => {
                $(
                    impl Int for $tpe {
                        impl_integer_functions!(
                            |s: &Self| *s, |x| x as $tpe
                        );
                    }
                )*
            };
        }

        impl_integer!(u8, u16, u32, u64, u128, i8, i16, i32, i64, i128, usize, isize);
    }
}
pub mod scanner {
    use crate::arraylist::List;
    use std::io::{stdin, BufReader, Bytes, Read, Stdin};
    use std::str::FromStr;

    pub struct Scanner {
        buf: Bytes<BufReader<Stdin>>,
    }

    impl Scanner {
        pub fn new() -> Scanner {
            Scanner {
                buf: BufReader::new(stdin()).bytes(),
            }
        }

        #[inline]
        fn token<T: std::iter::FromIterator<char>>(&mut self) -> T {
            self.buf
                .by_ref()
                .map(|c| c.unwrap() as char)
                .skip_while(|c| c.is_whitespace())
                .take_while(|c| !c.is_whitespace())
                .collect()
        }

        #[inline]
        pub fn read<T: FromStr>(&mut self) -> T {
            self.string().parse().ok().unwrap()
        }

        #[inline]
        pub fn readn<T: FromStr>(&mut self, n: isize) -> List<T> {
            (0..n).map(|_| self.read::<T>()).collect()
        }

        #[inline]
        pub fn string(&mut self) -> String {
            self.token()
        }

        #[inline]
        pub fn int(&mut self) -> isize {
            self.read()
        }
    }
}