// The main code is at the very bottom.

#[allow(unused_imports)]
use {
  lib::byte::ByteChar,
  std::cell::{Cell, RefCell},
  std::cmp::{
    self,
    Ordering::{self, *},
    Reverse,
  },
  std::collections::*,
  std::convert::identity,
  std::fmt::{self, Debug, Display, Formatter},
  std::io::prelude::*,
  std::iter::{self, FromIterator},
  std::marker::PhantomData,
  std::mem,
  std::num::Wrapping,
  std::ops::{Range, RangeFrom, RangeInclusive, RangeTo, RangeToInclusive},
  std::process,
  std::rc::Rc,
  std::thread,
  std::time::{Duration, Instant},
  std::{char, f32, f64, i128, i16, i32, i64, i8, isize, str, u128, u16, u32, u64, u8, usize},
};

#[allow(unused_imports)]
#[macro_use]
pub mod lib {
  pub mod byte {
    pub use self::byte_char::*;

    mod byte_char {
      use std::error::Error;
      use std::fmt::{self, Debug, Display, Formatter};
      use std::str::FromStr;

      #[derive(Clone, Copy, Default, PartialEq, Eq, PartialOrd, Ord, Hash)]
      #[repr(transparent)]
      pub struct ByteChar(pub u8);

      impl Debug for ByteChar {
        fn fmt(&self, f: &mut Formatter) -> fmt::Result {
          write!(f, "b'{}'", self.0 as char)
        }
      }

      impl Display for ByteChar {
        fn fmt(&self, f: &mut Formatter) -> fmt::Result {
          write!(f, "{}", self.0 as char)
        }
      }

      impl FromStr for ByteChar {
        type Err = ParseByteCharError;

        fn from_str(s: &str) -> Result<ByteChar, ParseByteCharError> {
          match s.as_bytes().len() {
            1 => Ok(ByteChar(s.as_bytes()[0])),
            0 => Err(ParseByteCharErrorKind::EmptyStr.into()),
            _ => Err(ParseByteCharErrorKind::TooManyBytes.into()),
          }
        }
      }

      #[derive(Clone, Copy, PartialEq, Eq, Hash, Debug)]
      pub struct ParseByteCharError {
        kind: ParseByteCharErrorKind,
      }

      impl Display for ParseByteCharError {
        fn fmt(&self, f: &mut Formatter) -> fmt::Result {
          f.write_str(match self.kind {
            ParseByteCharErrorKind::EmptyStr => "empty string",
            ParseByteCharErrorKind::TooManyBytes => "too many bytes",
          })
        }
      }

      impl Error for ParseByteCharError {}

      #[derive(Clone, Copy, PartialEq, Eq, Hash, Debug)]
      enum ParseByteCharErrorKind {
        EmptyStr,
        TooManyBytes,
      }

      impl From<ParseByteCharErrorKind> for ParseByteCharError {
        fn from(kind: ParseByteCharErrorKind) -> ParseByteCharError {
          ParseByteCharError { kind }
        }
      }
    }
  }

  pub mod io {
    pub use self::scanner::*;

    mod scanner {
      use std::io::{self, BufRead};
      use std::iter;
      use std::str::FromStr;

      #[derive(Debug)]
      pub struct Scanner<R> {
        reader: R,
        buf: String,
        pos: usize,
      }

      impl<R: BufRead> Scanner<R> {
        pub fn new(reader: R) -> Self {
          Scanner {
            reader,
            buf: String::new(),
            pos: 0,
          }
        }

        pub fn next(&mut self) -> io::Result<&str> {
          let start = loop {
            match self.rest().find(|c| c != ' ') {
              Some(i) => break i,
              None => self.fill_buf()?,
            }
          };
          self.pos += start;
          let len = self.rest().find(' ').unwrap_or(self.rest().len());
          let s = &self.buf[self.pos..][..len]; // self.rest()[..len]
          self.pos += len;
          Ok(s)
        }

        pub fn parse_next<T>(&mut self) -> io::Result<Result<T, T::Err>>
        where
          T: FromStr,
        {
          Ok(self.next()?.parse())
        }

        pub fn parse_next_n<T>(&mut self, n: usize) -> io::Result<Result<Vec<T>, T::Err>>
        where
          T: FromStr,
        {
          iter::repeat_with(|| self.parse_next()).take(n).collect()
        }

        pub fn map_next_bytes<T, F>(&mut self, mut f: F) -> io::Result<Vec<T>>
        where
          F: FnMut(u8) -> T,
        {
          Ok(self.next()?.bytes().map(&mut f).collect())
        }

        pub fn map_next_bytes_n<T, F>(&mut self, n: usize, mut f: F) -> io::Result<Vec<Vec<T>>>
        where
          F: FnMut(u8) -> T,
        {
          iter::repeat_with(|| self.map_next_bytes(&mut f))
            .take(n)
            .collect()
        }

        fn rest(&self) -> &str {
          &self.buf[self.pos..]
        }

        fn fill_buf(&mut self) -> io::Result<()> {
          self.buf.clear();
          self.pos = 0;
          let read = self.reader.read_line(&mut self.buf)?;
          if read == 0 {
            return Err(io::ErrorKind::UnexpectedEof.into());
          }
          if *self.buf.as_bytes().last().unwrap() == b'\n' {
            self.buf.pop();
          }
          Ok(())
        }
      }
    }
  }
}

#[allow(dead_code)]
mod ac_library_rs {

  pub mod modint {

    use crate::ac_library_rs::internal_math;
    use std::{
      cell::RefCell,
      convert::{Infallible, TryInto as _},
      fmt,
      hash::{Hash, Hasher},
      iter::{Product, Sum},
      marker::PhantomData,
      ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Sub, SubAssign},
      str::FromStr,
      sync::atomic::{self, AtomicU32, AtomicU64},
      thread::LocalKey,
    };

    pub type ModInt1000000007 = StaticModInt<Mod1000000007>;
    pub type ModInt998244353 = StaticModInt<Mod998244353>;
    pub type ModInt = DynamicModInt<DefaultId>;

    #[derive(Copy, Clone, Eq, PartialEq)]
    #[repr(transparent)]
    pub struct StaticModInt<M> {
      val: u32,
      phantom: PhantomData<fn() -> M>,
    }

    impl<M: Modulus> StaticModInt<M> {
      #[inline(always)]
      pub fn modulus() -> u32 {
        M::VALUE
      }

      #[inline]
      pub fn new<T: RemEuclidU32>(val: T) -> Self {
        Self::raw(val.rem_euclid_u32(M::VALUE))
      }

      #[inline]
      pub fn raw(val: u32) -> Self {
        Self {
          val,
          phantom: PhantomData,
        }
      }

      #[inline]
      pub fn val(self) -> u32 {
        self.val
      }

      #[inline]
      pub fn pow(self, n: u64) -> Self {
        <Self as ModIntBase>::pow(self, n)
      }

      #[inline]
      pub fn inv(self) -> Self {
        if M::HINT_VALUE_IS_PRIME {
          if self.val() == 0 {
            panic!("attempt to divide by zero");
          }
          debug_assert!(
            internal_math::is_prime(M::VALUE.try_into().unwrap()),
            "{} is not a prime number",
            M::VALUE,
          );
          self.pow((M::VALUE - 2).into())
        } else {
          Self::inv_for_non_prime_modulus(self)
        }
      }
    }

    impl<M: Modulus> ModIntBase for StaticModInt<M> {
      #[inline(always)]
      fn modulus() -> u32 {
        Self::modulus()
      }

      #[inline]
      fn raw(val: u32) -> Self {
        Self::raw(val)
      }

      #[inline]
      fn val(self) -> u32 {
        self.val()
      }

      #[inline]
      fn inv(self) -> Self {
        self.inv()
      }
    }

    pub trait Modulus: 'static + Copy + Eq {
      const VALUE: u32;
      const HINT_VALUE_IS_PRIME: bool;

      fn butterfly_cache() -> &'static LocalKey<RefCell<Option<ButterflyCache<Self>>>>;
    }

    #[derive(Copy, Clone, Ord, PartialOrd, Eq, PartialEq, Hash, Debug)]
    pub enum Mod1000000007 {}

    impl Modulus for Mod1000000007 {
      const VALUE: u32 = 1_000_000_007;
      const HINT_VALUE_IS_PRIME: bool = true;

      fn butterfly_cache() -> &'static LocalKey<RefCell<Option<ButterflyCache<Self>>>> {
        thread_local! {
            static BUTTERFLY_CACHE: RefCell<Option<ButterflyCache<Mod1000000007>>> = RefCell::default();
        }
        &BUTTERFLY_CACHE
      }
    }

    #[derive(Copy, Clone, Ord, PartialOrd, Eq, PartialEq, Hash, Debug)]
    pub enum Mod998244353 {}

    impl Modulus for Mod998244353 {
      const VALUE: u32 = 998_244_353;
      const HINT_VALUE_IS_PRIME: bool = true;

      fn butterfly_cache() -> &'static LocalKey<RefCell<Option<ButterflyCache<Self>>>> {
        thread_local! {
            static BUTTERFLY_CACHE: RefCell<Option<ButterflyCache<Mod998244353>>> = RefCell::default();
        }
        &BUTTERFLY_CACHE
      }
    }

    pub struct ButterflyCache<M> {
      pub(crate) sum_e: Vec<StaticModInt<M>>,
      pub(crate) sum_ie: Vec<StaticModInt<M>>,
    }

    #[derive(Copy, Clone, Eq, PartialEq)]
    #[repr(transparent)]
    pub struct DynamicModInt<I> {
      val: u32,
      phantom: PhantomData<fn() -> I>,
    }

    impl<I: Id> DynamicModInt<I> {
      #[inline]
      pub fn modulus() -> u32 {
        I::companion_barrett().umod()
      }

      #[inline]
      pub fn set_modulus(modulus: u32) {
        if modulus == 0 {
          panic!("the modulus must not be 0");
        }
        I::companion_barrett().update(modulus);
      }

      #[inline]
      pub fn new<T: RemEuclidU32>(val: T) -> Self {
        <Self as ModIntBase>::new(val)
      }

      #[inline]
      pub fn raw(val: u32) -> Self {
        Self {
          val,
          phantom: PhantomData,
        }
      }

      #[inline]
      pub fn val(self) -> u32 {
        self.val
      }

      #[inline]
      pub fn pow(self, n: u64) -> Self {
        <Self as ModIntBase>::pow(self, n)
      }

      #[inline]
      pub fn inv(self) -> Self {
        Self::inv_for_non_prime_modulus(self)
      }
    }

    impl<I: Id> ModIntBase for DynamicModInt<I> {
      #[inline]
      fn modulus() -> u32 {
        Self::modulus()
      }

      #[inline]
      fn raw(val: u32) -> Self {
        Self::raw(val)
      }

      #[inline]
      fn val(self) -> u32 {
        self.val()
      }

      #[inline]
      fn inv(self) -> Self {
        self.inv()
      }
    }

    pub trait Id: 'static + Copy + Eq {
      fn companion_barrett() -> &'static Barrett;
    }

    #[derive(Copy, Clone, Ord, PartialOrd, Eq, PartialEq, Hash, Debug)]
    pub enum DefaultId {}

    impl Id for DefaultId {
      fn companion_barrett() -> &'static Barrett {
        static BARRETT: Barrett = Barrett::default();
        &BARRETT
      }
    }

    pub struct Barrett {
      m: AtomicU32,
      im: AtomicU64,
    }

    impl Barrett {
      #[inline]
      pub const fn new(m: u32) -> Self {
        Self {
          m: AtomicU32::new(m),
          im: AtomicU64::new((-1i64 as u64 / m as u64).wrapping_add(1)),
        }
      }

      #[inline]
      const fn default() -> Self {
        Self::new(998_244_353)
      }

      #[inline]
      fn update(&self, m: u32) {
        let im = (-1i64 as u64 / m as u64).wrapping_add(1);
        self.m.store(m, atomic::Ordering::SeqCst);
        self.im.store(im, atomic::Ordering::SeqCst);
      }

      #[inline]
      fn umod(&self) -> u32 {
        self.m.load(atomic::Ordering::SeqCst)
      }

      #[inline]
      fn mul(&self, a: u32, b: u32) -> u32 {
        let m = self.m.load(atomic::Ordering::SeqCst);
        let im = self.im.load(atomic::Ordering::SeqCst);
        internal_math::mul_mod(a, b, m, im)
      }
    }

    impl Default for Barrett {
      #[inline]
      fn default() -> Self {
        Self::default()
      }
    }

    pub trait ModIntBase:
      Default
      + FromStr
      + From<i8>
      + From<i16>
      + From<i32>
      + From<i64>
      + From<i128>
      + From<isize>
      + From<u8>
      + From<u16>
      + From<u32>
      + From<u64>
      + From<u128>
      + From<usize>
      + Copy
      + Eq
      + Hash
      + fmt::Display
      + fmt::Debug
      + Neg<Output = Self>
      + Add<Output = Self>
      + Sub<Output = Self>
      + Mul<Output = Self>
      + Div<Output = Self>
      + AddAssign
      + SubAssign
      + MulAssign
      + DivAssign
    {
      fn modulus() -> u32;

      fn raw(val: u32) -> Self;

      fn val(self) -> u32;

      fn inv(self) -> Self;

      #[inline]
      fn new<T: RemEuclidU32>(val: T) -> Self {
        Self::raw(val.rem_euclid_u32(Self::modulus()))
      }

      #[inline]
      fn pow(self, mut n: u64) -> Self {
        let mut x = self;
        let mut r = Self::raw(1);
        while n > 0 {
          if n & 1 == 1 {
            r *= x;
          }
          x *= x;
          n >>= 1;
        }
        r
      }
    }

    pub trait RemEuclidU32 {
      fn rem_euclid_u32(self, modulus: u32) -> u32;
    }

    macro_rules! impl_rem_euclid_u32_for_small_signed {
        ($($ty:tt),*) => {
            $(
                impl RemEuclidU32 for $ty {
                    #[inline]
                    fn rem_euclid_u32(self, modulus: u32) -> u32 {
                        (self as i64).rem_euclid(i64::from(modulus)) as _
                    }
                }
            )*
        }
    }

    impl_rem_euclid_u32_for_small_signed!(i8, i16, i32, i64, isize);

    impl RemEuclidU32 for i128 {
      #[inline]
      fn rem_euclid_u32(self, modulus: u32) -> u32 {
        self.rem_euclid(i128::from(modulus)) as _
      }
    }

    macro_rules! impl_rem_euclid_u32_for_small_unsigned {
        ($($ty:tt),*) => {
            $(
                impl RemEuclidU32 for $ty {
                    #[inline]
                    fn rem_euclid_u32(self, modulus: u32) -> u32 {
                        self as u32 % modulus
                    }
                }
            )*
        }
    }

    macro_rules! impl_rem_euclid_u32_for_large_unsigned {
        ($($ty:tt),*) => {
            $(
                impl RemEuclidU32 for $ty {
                    #[inline]
                    fn rem_euclid_u32(self, modulus: u32) -> u32 {
                        (self % (modulus as $ty)) as _
                    }
                }
            )*
        }
    }

    impl_rem_euclid_u32_for_small_unsigned!(u8, u16, u32);
    impl_rem_euclid_u32_for_large_unsigned!(u64, u128);

    #[cfg(target_pointer_width = "32")]
    impl_rem_euclid_u32_for_small_unsigned!(usize);

    #[cfg(target_pointer_width = "64")]
    impl_rem_euclid_u32_for_large_unsigned!(usize);

    trait InternalImplementations: ModIntBase {
      #[inline]
      fn inv_for_non_prime_modulus(this: Self) -> Self {
        let (gcd, x) = internal_math::inv_gcd(this.val().into(), Self::modulus().into());
        if gcd != 1 {
          panic!("the multiplicative inverse does not exist");
        }
        Self::new(x)
      }

      #[inline]
      fn default_impl() -> Self {
        Self::raw(0)
      }

      #[inline]
      fn from_str_impl(s: &str) -> Result<Self, Infallible> {
        Ok(
          s.parse::<i64>()
            .map(Self::new)
            .unwrap_or_else(|_| todo!("parsing as an arbitrary precision integer?")),
        )
      }

      #[inline]
      fn hash_impl(this: &Self, state: &mut impl Hasher) {
        this.val().hash(state)
      }

      #[inline]
      fn display_impl(this: &Self, f: &mut fmt::Formatter) -> fmt::Result {
        fmt::Display::fmt(&this.val(), f)
      }

      #[inline]
      fn debug_impl(this: &Self, f: &mut fmt::Formatter) -> fmt::Result {
        fmt::Debug::fmt(&this.val(), f)
      }

      #[inline]
      fn neg_impl(this: Self) -> Self {
        Self::sub_impl(Self::raw(0), this)
      }

      #[inline]
      fn add_impl(lhs: Self, rhs: Self) -> Self {
        let modulus = Self::modulus();
        let mut val = lhs.val() + rhs.val();
        if val >= modulus {
          val -= modulus;
        }
        Self::raw(val)
      }

      #[inline]
      fn sub_impl(lhs: Self, rhs: Self) -> Self {
        let modulus = Self::modulus();
        let mut val = lhs.val().wrapping_sub(rhs.val());
        if val >= modulus {
          val = val.wrapping_add(modulus)
        }
        Self::raw(val)
      }

      fn mul_impl(lhs: Self, rhs: Self) -> Self;

      #[inline]
      fn div_impl(lhs: Self, rhs: Self) -> Self {
        Self::mul_impl(lhs, rhs.inv())
      }
    }

    impl<M: Modulus> InternalImplementations for StaticModInt<M> {
      #[inline]
      fn mul_impl(lhs: Self, rhs: Self) -> Self {
        Self::raw((u64::from(lhs.val()) * u64::from(rhs.val()) % u64::from(M::VALUE)) as u32)
      }
    }

    impl<I: Id> InternalImplementations for DynamicModInt<I> {
      #[inline]
      fn mul_impl(lhs: Self, rhs: Self) -> Self {
        Self::raw(I::companion_barrett().mul(lhs.val, rhs.val))
      }
    }

    macro_rules! impl_basic_traits {
        () => {};
        (impl <$generic_param:ident : $generic_param_bound:tt> _ for $self:ty; $($rest:tt)*) => {
            impl <$generic_param: $generic_param_bound> Default for $self {
                #[inline]
                fn default() -> Self {
                    Self::default_impl()
                }
            }

            impl <$generic_param: $generic_param_bound> FromStr for $self {
                type Err = Infallible;

                #[inline]
                fn from_str(s: &str) -> Result<Self, Infallible> {
                    Self::from_str_impl(s)
                }
            }

            impl<$generic_param: $generic_param_bound, V: RemEuclidU32> From<V> for $self {
                #[inline]
                fn from(from: V) -> Self {
                    Self::new(from)
                }
            }

            #[allow(clippy::derive_hash_xor_eq)]
            impl<$generic_param: $generic_param_bound> Hash for $self {
                #[inline]
                fn hash<H: Hasher>(&self, state: &mut H) {
                    Self::hash_impl(self, state)
                }
            }

            impl<$generic_param: $generic_param_bound> fmt::Display for $self {
                #[inline]
                fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
                    Self::display_impl(self, f)
                }
            }

            impl<$generic_param: $generic_param_bound> fmt::Debug for $self {
                #[inline]
                fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
                    Self::debug_impl(self, f)
                }
            }

            impl<$generic_param: $generic_param_bound> Neg for $self {
                type Output = $self;

                #[inline]
                fn neg(self) -> $self {
                    Self::neg_impl(self)
                }
            }

            impl<$generic_param: $generic_param_bound> Neg for &'_ $self {
                type Output = $self;

                #[inline]
                fn neg(self) -> $self {
                    <$self>::neg_impl(*self)
                }
            }

            impl_basic_traits!($($rest)*);
        };
    }

    impl_basic_traits! {
        impl <M: Modulus> _ for StaticModInt<M> ;
        impl <I: Id     > _ for DynamicModInt<I>;
    }

    macro_rules! impl_bin_ops {
        () => {};
        (for<$($generic_param:ident : $generic_param_bound:tt),*> <$lhs_ty:ty> ~ <$rhs_ty:ty> -> $output:ty { { $lhs_body:expr } ~ { $rhs_body:expr } } $($rest:tt)*) => {
            impl <$($generic_param: $generic_param_bound),*> Add<$rhs_ty> for $lhs_ty {
                type Output = $output;

                #[inline]
                fn add(self, rhs: $rhs_ty) -> $output {
                    <$output>::add_impl(apply($lhs_body, self), apply($rhs_body, rhs))
                }
            }

            impl <$($generic_param: $generic_param_bound),*> Sub<$rhs_ty> for $lhs_ty {
                type Output = $output;

                #[inline]
                fn sub(self, rhs: $rhs_ty) -> $output {
                    <$output>::sub_impl(apply($lhs_body, self), apply($rhs_body, rhs))
                }
            }

            impl <$($generic_param: $generic_param_bound),*> Mul<$rhs_ty> for $lhs_ty {
                type Output = $output;

                #[inline]
                fn mul(self, rhs: $rhs_ty) -> $output {
                    <$output>::mul_impl(apply($lhs_body, self), apply($rhs_body, rhs))
                }
            }

            impl <$($generic_param: $generic_param_bound),*> Div<$rhs_ty> for $lhs_ty {
                type Output = $output;

                #[inline]
                fn div(self, rhs: $rhs_ty) -> $output {
                    <$output>::div_impl(apply($lhs_body, self), apply($rhs_body, rhs))
                }
            }

            impl_bin_ops!($($rest)*);
        };
    }

    macro_rules! impl_assign_ops {
        () => {};
        (for<$($generic_param:ident : $generic_param_bound:tt),*> <$lhs_ty:ty> ~= <$rhs_ty:ty> { _ ~= { $rhs_body:expr } } $($rest:tt)*) => {
            impl <$($generic_param: $generic_param_bound),*> AddAssign<$rhs_ty> for $lhs_ty {
                #[inline]
                fn add_assign(&mut self, rhs: $rhs_ty) {
                    *self = *self + apply($rhs_body, rhs);
                }
            }

            impl <$($generic_param: $generic_param_bound),*> SubAssign<$rhs_ty> for $lhs_ty {
                #[inline]
                fn sub_assign(&mut self, rhs: $rhs_ty) {
                    *self = *self - apply($rhs_body, rhs);
                }
            }

            impl <$($generic_param: $generic_param_bound),*> MulAssign<$rhs_ty> for $lhs_ty {
                #[inline]
                fn mul_assign(&mut self, rhs: $rhs_ty) {
                    *self = *self * apply($rhs_body, rhs);
                }
            }

            impl <$($generic_param: $generic_param_bound),*> DivAssign<$rhs_ty> for $lhs_ty {
                #[inline]
                fn div_assign(&mut self, rhs: $rhs_ty) {
                    *self = *self / apply($rhs_body, rhs);
                }
            }

            impl_assign_ops!($($rest)*);
        };
    }

    #[inline]
    fn apply<F: FnOnce(X) -> O, X, O>(f: F, x: X) -> O {
      f(x)
    }

    impl_bin_ops! {
        for<M: Modulus> <StaticModInt<M>     > ~ <StaticModInt<M>     > -> StaticModInt<M>  { { |x| x  } ~ { |x| x  } }
        for<M: Modulus> <StaticModInt<M>     > ~ <&'_ StaticModInt<M> > -> StaticModInt<M>  { { |x| x  } ~ { |&x| x } }
        for<M: Modulus> <&'_ StaticModInt<M> > ~ <StaticModInt<M>     > -> StaticModInt<M>  { { |&x| x } ~ { |x| x  } }
        for<M: Modulus> <&'_ StaticModInt<M> > ~ <&'_ StaticModInt<M> > -> StaticModInt<M>  { { |&x| x } ~ { |&x| x } }
        for<I: Id     > <DynamicModInt<I>    > ~ <DynamicModInt<I>    > -> DynamicModInt<I> { { |x| x  } ~ { |x| x  } }
        for<I: Id     > <DynamicModInt<I>    > ~ <&'_ DynamicModInt<I>> -> DynamicModInt<I> { { |x| x  } ~ { |&x| x } }
        for<I: Id     > <&'_ DynamicModInt<I>> ~ <DynamicModInt<I>    > -> DynamicModInt<I> { { |&x| x } ~ { |x| x  } }
        for<I: Id     > <&'_ DynamicModInt<I>> ~ <&'_ DynamicModInt<I>> -> DynamicModInt<I> { { |&x| x } ~ { |&x| x } }

        for<M: Modulus, T: RemEuclidU32> <StaticModInt<M>     > ~ <T> -> StaticModInt<M>  { { |x| x  } ~ { StaticModInt::<M>::new } }
        for<I: Id     , T: RemEuclidU32> <DynamicModInt<I>    > ~ <T> -> DynamicModInt<I> { { |x| x  } ~ { DynamicModInt::<I>::new } }
    }

    impl_assign_ops! {
        for<M: Modulus> <StaticModInt<M> > ~= <StaticModInt<M>     > { _ ~= { |x| x  } }
        for<M: Modulus> <StaticModInt<M> > ~= <&'_ StaticModInt<M> > { _ ~= { |&x| x } }
        for<I: Id     > <DynamicModInt<I>> ~= <DynamicModInt<I>    > { _ ~= { |x| x  } }
        for<I: Id     > <DynamicModInt<I>> ~= <&'_ DynamicModInt<I>> { _ ~= { |&x| x } }

        for<M: Modulus, T: RemEuclidU32> <StaticModInt<M> > ~= <T> { _ ~= { StaticModInt::<M>::new } }
        for<I: Id,      T: RemEuclidU32> <DynamicModInt<I>> ~= <T> { _ ~= { DynamicModInt::<I>::new } }
    }

    macro_rules! impl_folding {
        () => {};
        (impl<$generic_param:ident : $generic_param_bound:tt> $trait:ident<_> for $self:ty { fn $method:ident(_) -> _ { _($unit:expr, $op:expr) } } $($rest:tt)*) => {
            impl<$generic_param: $generic_param_bound> $trait<Self> for $self {
                #[inline]
                fn $method<S>(iter: S) -> Self
                where
                    S: Iterator<Item = Self>,
                {
                    iter.fold($unit, $op)
                }
            }

            impl<'a, $generic_param: $generic_param_bound> $trait<&'a Self> for $self {
                #[inline]
                fn $method<S>(iter: S) -> Self
                where
                    S: Iterator<Item = &'a Self>,
                {
                    iter.fold($unit, $op)
                }
            }

            impl_folding!($($rest)*);
        };
    }

    impl_folding! {
        impl<M: Modulus> Sum<_>     for StaticModInt<M>  { fn sum(_)     -> _ { _(Self::raw(0), Add::add) } }
        impl<M: Modulus> Product<_> for StaticModInt<M>  { fn product(_) -> _ { _(Self::raw(1), Mul::mul) } }
        impl<I: Id     > Sum<_>     for DynamicModInt<I> { fn sum(_)     -> _ { _(Self::raw(0), Add::add) } }
        impl<I: Id     > Product<_> for DynamicModInt<I> { fn product(_) -> _ { _(Self::raw(1), Mul::mul) } }
    }
  }

  pub(crate) mod internal_math {

    #![allow(dead_code)]
    use std::mem::swap;

    pub(crate) fn safe_mod(mut x: i64, m: i64) -> i64 {
      x %= m;
      if x < 0 {
        x += m;
      }
      x
    }

    pub(crate) struct Barrett {
      pub(crate) _m: u32,
      pub(crate) im: u64,
    }

    impl Barrett {
      pub(crate) fn new(m: u32) -> Barrett {
        Barrett {
          _m: m,
          im: (-1i64 as u64 / m as u64).wrapping_add(1),
        }
      }

      pub(crate) fn umod(&self) -> u32 {
        self._m
      }

      #[allow(clippy::many_single_char_names)]
      pub(crate) fn mul(&self, a: u32, b: u32) -> u32 {
        mul_mod(a, b, self._m, self.im)
      }
    }

    #[allow(clippy::many_single_char_names)]
    pub(crate) fn mul_mod(a: u32, b: u32, m: u32, im: u64) -> u32 {
      let mut z = a as u64;
      z *= b as u64;
      let x = (((z as u128) * (im as u128)) >> 64) as u64;
      let mut v = z.wrapping_sub(x.wrapping_mul(m as u64)) as u32;
      if m <= v {
        v = v.wrapping_add(m);
      }
      v
    }

    #[allow(clippy::many_single_char_names)]
    pub(crate) fn pow_mod(x: i64, mut n: i64, m: i32) -> i64 {
      if m == 1 {
        return 0;
      }
      let _m = m as u32;
      let mut r: u64 = 1;
      let mut y: u64 = safe_mod(x, m as i64) as u64;
      while n != 0 {
        if (n & 1) > 0 {
          r = (r * y) % (_m as u64);
        }
        y = (y * y) % (_m as u64);
        n >>= 1;
      }
      r as i64
    }

    pub(crate) fn is_prime(n: i32) -> bool {
      let n = n as i64;
      match n {
        _ if n <= 1 => return false,
        2 | 7 | 61 => return true,
        _ if n % 2 == 0 => return false,
        _ => {}
      }
      let mut d = n - 1;
      while d % 2 == 0 {
        d /= 2;
      }
      for &a in &[2, 7, 61] {
        let mut t = d;
        let mut y = pow_mod(a, t, n as i32);
        while t != n - 1 && y != 1 && y != n - 1 {
          y = y * y % n;
          t <<= 1;
        }
        if y != n - 1 && t % 2 == 0 {
          return false;
        }
      }
      true
    }

    #[allow(clippy::many_single_char_names)]
    pub(crate) fn inv_gcd(a: i64, b: i64) -> (i64, i64) {
      let a = safe_mod(a, 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)
    }

    pub(crate) 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| pow_mod(g, ((m - 1) / divs[i]) as i64, m) != 1) {
          break g as i32;
        }
        g += 1;
      }
    }
  }

  pub use modint::{
    Barrett, ButterflyCache, DefaultId, DynamicModInt, Id, Mod1000000007, Mod998244353, ModInt,
    ModInt1000000007, ModInt998244353, Modulus, RemEuclidU32, StaticModInt,
  };
}

#[allow(unused_macros)]
macro_rules! eprint {
  ($($arg:tt)*) => {
    if cfg!(debug_assertions) {
      std::eprint!($($arg)*)
    }
  };
}
#[allow(unused_macros)]
macro_rules! eprintln {
  ($($arg:tt)*) => {
    if cfg!(debug_assertions) {
      std::eprintln!($($arg)*)
    }
  };
}
#[allow(unused_macros)]
macro_rules! dbg {
  ($($arg:tt)*) => {
    if cfg!(debug_assertions) {
      std::dbg!($($arg)*)
    } else {
      ($($arg)*)
    }
  };
}

const CUSTOM_STACK_SIZE_MIB: Option<usize> = Some(1024);
const INTERACTIVE: bool = false;

fn main() -> std::io::Result<()> {
  match CUSTOM_STACK_SIZE_MIB {
    Some(stack_size_mib) => std::thread::Builder::new()
      .name("run_solver".to_owned())
      .stack_size(stack_size_mib * 1024 * 1024)
      .spawn(run_solver)?
      .join()
      .unwrap(),
    None => run_solver(),
  }
}

fn run_solver() -> std::io::Result<()> {
  let stdin = std::io::stdin();
  let reader = stdin.lock();
  let stdout = std::io::stdout();
  let writer = stdout.lock();
  macro_rules! with_wrapper {
    ($($wrapper:expr)?) => {{
      let mut writer = $($wrapper)?(writer);
      solve(reader, &mut writer)?;
      writer.flush()
    }};
  }
  if cfg!(debug_assertions) || INTERACTIVE {
    with_wrapper!()
  } else {
    with_wrapper!(std::io::BufWriter::new)
  }
}

fn solve<R, W>(reader: R, mut writer: W) -> std::io::Result<()>
where
  R: BufRead,
  W: Write,
{
  let mut _scanner = lib::io::Scanner::new(reader);
  #[allow(unused_macros)]
  macro_rules! scan {
    ($T:ty) => {
      _scanner.parse_next::<$T>()?.unwrap()
    };
    ($($T:ty),+) => {
      ($(scan!($T)),+)
    };
    ($T:ty; $n:expr) => {
      _scanner.parse_next_n::<$T>($n)?.unwrap()
    };
    ($($T:ty),+; $n:expr) => {
      iter::repeat_with(|| -> std::io::Result<_> { Ok(($(scan!($T)),+)) })
        .take($n)
        .collect::<std::io::Result<Vec<_>>>()?
    };
  }
  #[allow(unused_macros)]
  macro_rules! scan_bytes_map {
    ($f:expr) => {
      _scanner.map_next_bytes($f)?
    };
    ($f:expr; $n:expr) => {
      _scanner.map_next_bytes_n($n, $f)?
    };
  }
  #[allow(unused_macros)]
  macro_rules! print {
    ($($arg:tt)*) => {
      write!(writer, $($arg)*)?
    };
  }
  #[allow(unused_macros)]
  macro_rules! println {
    ($($arg:tt)*) => {
      writeln!(writer, $($arg)*)?
    };
  }
  #[allow(unused_macros)]
  macro_rules! answer {
    ($($arg:tt)*) => {{
      println!($($arg)*);
      return Ok(());
    }};
  }
  {
    use ac_library_rs::ModInt1000000007 as Mint;

    let t = scan!(usize);
    for _ in 0..t {
      let n = scan!(usize);
      let a = scan!(u64; n);

      let ans = a
        .into_iter()
        .map(|a_i| Mint::new(a_i))
        .fold(Mint::new(0), |x, y| x + y + x * y);
      println!("{}", ans);
    }
  }
  #[allow(unreachable_code)]
  Ok(())
}