#![allow(unused_imports)]
pub use __cargo_equip::prelude::*;

use acl_modint::ModInt1000000007;
#[allow(unused_imports)]
use proconio::fastout;
use proconio::input;

/*#[fastout]
fn main() {
    input!{
        _n: u64,
        m: u64,
    };
    let two = ModInt1000000007::new(2);
    println!("{}",(two.pow(m) - 1) / 2);
}*/
fn main() {
    let __proconio_stdout = ::std::io::stdout();
    let mut __proconio_stdout = ::std::io::BufWriter::new(__proconio_stdout.lock());
    let __proconio_res = {
        input! { _n : u64 , m : u64 , };
        let two = ModInt1000000007::new(2);
        <::std::io::BufWriter<::std::io::StdoutLock> as ::std::io::Write>::write_fmt(
            &mut __proconio_stdout,
            format_args!(concat!("{}", "\n"), (two.pow(m) - 1) / 2),
        )
        .unwrap();
    };
    <::std::io::BufWriter<::std::io::StdoutLock> as ::std::io::Write>::flush(
        &mut __proconio_stdout,
    )
    .unwrap();
    return __proconio_res;
}

// The following code was expanded by `cargo-equip`.

///  # Bundled libraries
/// 
///  - `ac-library-rs-parted-internal-math 0.1.0 (git+https://github.com/qryxip/ac-library-rs-parted#77261929d6551609cf352f4f9e05b34bafd5a8f7)` licensed under `CC0-1.0`           as `crate::__cargo_equip::crates::__ac_library_rs_parted_internal_math_0_1_0`
///  - `ac-library-rs-parted-modint 0.1.0 (git+https://github.com/qryxip/ac-library-rs-parted#77261929d6551609cf352f4f9e05b34bafd5a8f7)`        licensed under `CC0-1.0`           as `crate::__cargo_equip::crates::acl_modint`
///  - `lazy_static 1.4.0 (registry+https://github.com/rust-lang/crates.io-index)`                                                              licensed under `MIT/Apache-2.0`    as `crate::__cargo_equip::crates::__lazy_static_1_4_0`
///  - `proconio 0.3.6 (registry+https://github.com/rust-lang/crates.io-index)`                                                                 licensed under `MIT OR Apache-2.0` as `crate::__cargo_equip::crates::proconio`
/// 
///  # Procedural macros
/// 
///  - `proconio-derive 0.1.9 (registry+https://github.com/rust-lang/crates.io-index)` licensed under `MIT OR Apache-2.0`
/// 
///  # License and Copyright Notices
/// 
///  - `lazy_static 1.4.0 (registry+https://github.com/rust-lang/crates.io-index)`
/// 
///      ```text
///      Copyright (c) 2010 The Rust Project Developers
/// 
///      Permission is hereby granted, free of charge, to any
///      person obtaining a copy of this software and associated
///      documentation files (the "Software"), to deal in the
///      Software without restriction, including without
///      limitation the rights to use, copy, modify, merge,
///      publish, distribute, sublicense, and/or sell copies of
///      the Software, and to permit persons to whom the Software
///      is furnished to do so, subject to the following
///      conditions:
/// 
///      The above copyright notice and this permission notice
///      shall be included in all copies or substantial portions
///      of the Software.
/// 
///      THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF
///      ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED
///      TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A
///      PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT
///      SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
///      CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
///      OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR
///      IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
///      DEALINGS IN THE SOFTWARE.
///      ```
/// 
///  - `proconio 0.3.6 (registry+https://github.com/rust-lang/crates.io-index)`
/// 
///      ```text
///      The MIT License
///      Copyright 2019 (C) statiolake <statiolake@gmail.com>
/// 
///      Permission is hereby granted, free of charge, to any person obtaining a copy of
///      this software and associated documentation files (the "Software"), to deal in
///      the Software without restriction, including without limitation the rights to
///      use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
///      the Software, and to permit persons to whom the Software is furnished to do so,
///      subject to the following conditions:
/// 
///      The above copyright notice and this permission notice shall be included in all
///      copies or substantial portions of the Software.
/// 
///      THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
///      IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS
///      FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR
///      COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER
///      IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
///      CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
/// 
///      Copyright for original `input!` macro is held by Hideyuki Tanaka, 2019.  The
///      original macro is licensed under BSD 3-clause license.
/// 
///      Redistribution and use in source and binary forms, with or without
///      modification, are permitted provided that the following conditions are met:
/// 
///      1. Redistributions of source code must retain the above copyright notice, this
///         list of conditions and the following disclaimer.
/// 
///      2. Redistributions in binary form must reproduce the above copyright notice,
///         this list of conditions and the following disclaimer in the documentation
///         and/or other materials provided with the distribution.
/// 
///      3. Neither the name of the copyright holder nor the names of its contributors
///         may be used to endorse or promote products derived from this software
///         without specific prior written permission.
/// 
///      THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
///      ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
///      WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
///      DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
///      FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
///      DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
///      SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
///      CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
///      OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
///      OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
///      ```
#[cfg_attr(any(), rustfmt::skip)]
#[allow(unused)]
mod __cargo_equip {
    pub(crate) mod crates {
        pub mod __ac_library_rs_parted_internal_math_0_1_0 {pub use self::internal_math::*;mod internal_math{#![allow(dead_code)]use std::mem::swap;pub fn safe_mod(mut x:i64,m:i64)->i64{x%=m;if x<0{x+=m;}x}pub struct Barrett{pub _m:u32,pub im:u64,}impl Barrett{pub fn new(m:u32)->Barrett{Barrett{_m:m,im:(-1i64 as u64/m as u64).wrapping_add(1),}}pub fn umod(&self)->u32{self._m}#[allow(clippy::many_single_char_names)]pub fn mul(&self,a:u32,b:u32)->u32{mul_mod(a,b,self._m,self.im)}}#[allow(clippy::many_single_char_names)]pub 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 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 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 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 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 mod acl_modint {use crate::__cargo_equip::preludes::acl_modint::*;use crate::__cargo_equip::crates::__ac_library_rs_parted_internal_math_0_1_0 as internal_math;pub use self::modint::*;mod modint{use crate::__cargo_equip::preludes::acl_modint::*;use super::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 sum_e:Vec<StaticModInt<M>>,pub 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 mod __lazy_static_1_4_0 {#![no_std]use crate::__cargo_equip::preludes::__lazy_static_1_4_0::*;pub use crate::__cargo_equip::macros::__lazy_static_1_4_0::*;#[path="inline_lazy.rs"]pub mod lazy{use crate::__cargo_equip::preludes::__lazy_static_1_4_0::*;extern crate core;extern crate std;use self::std::prelude::v1::*;use self::std::cell::Cell;use self::std::hint::unreachable_unchecked;use self::std::sync::Once;#[allow(deprecated)]pub use self::std::sync::ONCE_INIT;pub struct Lazy<T:Sync>(Cell<Option<T>>,Once);impl<T:Sync>Lazy<T>{#[allow(deprecated)]pub const INIT:Self=Lazy(Cell::new(None),ONCE_INIT);#[inline(always)]pub fn get<F>(&'static self,f:F)->&T where F:FnOnce()->T,{self.1.call_once(||{self.0.set(Some(f()));});unsafe{match*self.0.as_ptr(){Some(ref x)=>x,None=>{debug_assert!(false,"attempted to derefence an uninitialized lazy static. This is a bug");unreachable_unchecked()},}}}}unsafe impl<T:Sync>Sync for Lazy<T>{}#[macro_export]macro_rules!__cargo_equip_macro_def___lazy_static_1_4_0___lazy_static_create{($NAME:ident,$T:ty)=>{static$NAME:$crate::__cargo_equip::crates::__lazy_static_1_4_0::lazy::Lazy<$T> =$crate::__cargo_equip::crates::__lazy_static_1_4_0::lazy::Lazy::INIT;};}macro_rules!__lazy_static_create{($($tt:tt)*)=>(crate::__cargo_equip_macro_def___lazy_static_1_4_0___lazy_static_create!{$($tt)*})}}pub use core::ops::Deref as __Deref;#[macro_export(local_inner_macros)]macro_rules!__cargo_equip_macro_def___lazy_static_1_4_0___lazy_static_internal{($(#[$attr:meta])*($($vis:tt)*)static ref$N:ident:$T:ty=$e:expr;$($t:tt)*)=>{__lazy_static_internal!(@MAKE TY,$(#[$attr])*,($($vis)*),$N);__lazy_static_internal!(@TAIL,$N:$T=$e);lazy_static!($($t)*);};(@TAIL,$N:ident:$T:ty=$e:expr)=>{impl$crate::__cargo_equip::crates::__lazy_static_1_4_0::__Deref for$N{type Target=$T;fn deref(&self)->&$T{#[inline(always)]fn __static_ref_initialize()->$T{$e}#[inline(always)]fn __stability()->&'static$T{__lazy_static_create!(LAZY,$T);LAZY.get(__static_ref_initialize)}__stability()}}impl$crate::__cargo_equip::crates::__lazy_static_1_4_0::LazyStatic for$N{fn initialize(lazy:&Self){let _=&**lazy;}}};(@MAKE TY,$(#[$attr:meta])*,($($vis:tt)*),$N:ident)=>{#[allow(missing_copy_implementations)]#[allow(non_camel_case_types)]#[allow(dead_code)]$(#[$attr])*$($vis)*struct$N{__private_field:()}#[doc(hidden)]$($vis)*static$N:$N=$N{__private_field:()};};()=>()}macro_rules!__lazy_static_internal{($($tt:tt)*)=>(crate::__cargo_equip_macro_def___lazy_static_1_4_0___lazy_static_internal!{$($tt)*})}#[macro_export(local_inner_macros)]macro_rules!__cargo_equip_macro_def___lazy_static_1_4_0_lazy_static{($(#[$attr:meta])*static ref$N:ident:$T:ty=$e:expr;$($t:tt)*)=>{__lazy_static_internal!($(#[$attr])*()static ref$N:$T=$e;$($t)*);};($(#[$attr:meta])*pub static ref$N:ident:$T:ty=$e:expr;$($t:tt)*)=>{__lazy_static_internal!($(#[$attr])*(pub)static ref$N:$T=$e;$($t)*);};($(#[$attr:meta])*pub($($vis:tt)+)static ref$N:ident:$T:ty=$e:expr;$($t:tt)*)=>{__lazy_static_internal!($(#[$attr])*(pub($($vis)+))static ref$N:$T=$e;$($t)*);};()=>()}macro_rules!lazy_static{($($tt:tt)*)=>(crate::__cargo_equip_macro_def___lazy_static_1_4_0_lazy_static!{$($tt)*})}pub trait LazyStatic{fn initialize(lazy:&Self);}pub fn initialize<T:LazyStatic>(lazy:&T){LazyStatic::initialize(lazy);}}
        pub mod proconio {#![allow(clippy::needless_doctest_main,clippy::print_literal)]use crate::__cargo_equip::preludes::proconio::*;pub use crate::__cargo_equip::macros::proconio::*;pub use proconio_derive::*;pub mod marker{use crate::__cargo_equip::preludes::proconio::*;pub enum Chars{}pub enum Bytes{}pub enum Usize1{}pub enum Isize1{}}pub mod read{use crate::__cargo_equip::preludes::proconio::*;use crate::__cargo_equip::crates::proconio::marker::{Bytes,Chars,Isize1,Usize1};use crate::__cargo_equip::crates::proconio::source::{Readable,Source};use std::any::type_name;use std::fmt::Debug;use std::io::BufRead;use std::str::FromStr;impl<T:FromStr>Readable for T where T::Err:Debug,{type Output=T;fn read<R:BufRead,S:Source<R>>(source:&mut S)->T{let token=source.next_token_unwrap();match token.parse(){Ok(v)=>v,Err(e)=>panic!(concat!("failed to parse the input `{input}` ","to the value of type `{ty}`: {err:?}; ","ensure that the input format is collectly specified ","and that the input value must handle specified type.",),input=token,ty=type_name::<T>(),err=e,),}}}impl Readable for Chars{type Output=Vec<char>;fn read<R:BufRead,S:Source<R>>(source:&mut S)->Vec<char>{source.next_token_unwrap().chars().collect()}}impl Readable for Bytes{type Output=Vec<u8>;fn read<R:BufRead,S:Source<R>>(source:&mut S)->Vec<u8>{source.next_token_unwrap().bytes().collect()}}impl Readable for Usize1{type Output=usize;fn read<R:BufRead,S:Source<R>>(source:&mut S)->usize{usize::read(source)-1}}impl Readable for Isize1{type Output=isize;fn read<R:BufRead,S:Source<R>>(source:&mut S)->isize{isize::read(source)-1}}}pub mod source{use crate::__cargo_equip::preludes::proconio::*;use std::io::BufRead;pub mod line{use crate::__cargo_equip::preludes::proconio::*;use super::Source;use std::io::BufRead;use std::iter::Peekable;use std::str::SplitWhitespace;pub struct LineSource<R:BufRead>{tokens:Peekable<SplitWhitespace<'static>>,current_context:Box<str>,reader:R,}impl<R:BufRead>LineSource<R>{pub fn new(reader:R)->LineSource<R>{LineSource{current_context:"".to_string().into_boxed_str(),tokens:"".split_whitespace().peekable(),reader,}}fn prepare(&mut self){while self.tokens.peek().is_none(){let mut line=String::new();let num_bytes=self.reader.read_line(&mut line).expect("failed to get linel maybe an IO error.");if num_bytes==0{return;}self.current_context=line.into_boxed_str();self.tokens=unsafe{std::mem::transmute::<_,&'static str>(&*self.current_context)}.split_whitespace().peekable();}}}impl<R:BufRead>Source<R>for LineSource<R>{fn next_token(&mut self)->Option<&str>{self.prepare();self.tokens.next()}fn is_empty(&mut self)->bool{self.prepare();self.tokens.peek().is_none()}}use std::io::BufReader;impl<'a>From<&'a str>for LineSource<BufReader<&'a[u8]>>{fn from(s:&'a str)->LineSource<BufReader<&'a[u8]>>{LineSource::new(BufReader::new(s.as_bytes()))}}}pub mod once{use crate::__cargo_equip::preludes::proconio::*;use super::Source;use std::io::BufRead;use std::iter::Peekable;use std::marker::PhantomData;use std::str::SplitWhitespace;pub struct OnceSource<R:BufRead>{tokens:Peekable<SplitWhitespace<'static>>,context:Box<str>,_read:PhantomData<R>,}impl<R:BufRead>OnceSource<R>{pub fn new(mut source:R)->OnceSource<R>{let mut context=String::new();source.read_to_string(&mut context).expect("failed to read from source; maybe an IO error.");let context=context.into_boxed_str();let mut res=OnceSource{context,tokens:"".split_whitespace().peekable(),_read:PhantomData,};use std::mem;let context:&'static str=unsafe{mem::transmute(&*res.context)};res.tokens=context.split_whitespace().peekable();res}}impl<R:BufRead>Source<R>for OnceSource<R>{fn next_token(&mut self)->Option<&str>{self.tokens.next()}fn is_empty(&mut self)->bool{self.tokens.peek().is_none()}}use std::io::BufReader;impl<'a>From<&'a str>for OnceSource<BufReader<&'a[u8]>>{fn from(s:&'a str)->OnceSource<BufReader<&'a[u8]>>{OnceSource::new(BufReader::new(s.as_bytes()))}}}pub mod auto{use crate::__cargo_equip::preludes::proconio::*;#[cfg(debug_assertions)]pub use super::line::LineSource as AutoSource;#[cfg(not(debug_assertions))]pub use super::once::OnceSource as AutoSource;}pub trait Source<R:BufRead>{fn next_token(&mut self)->Option<&str>;fn is_empty(&mut self)->bool;fn next_token_unwrap(&mut self)->&str{self.next_token().expect(concat!("failed to get the next token; ","maybe reader reached an end of input. ","ensure that arguments for `input!` macro is correctly ","specified to match the problem input."))}}impl<R:BufRead,S:Source<R>>Source<R>for&'_ mut S{fn next_token(&mut self)->Option<&str>{(*self).next_token()}fn is_empty(&mut self)->bool{(*self).is_empty()}}pub trait Readable{type Output;fn read<R:BufRead,S:Source<R>>(source:&mut S)->Self::Output;}}use crate::__cargo_equip::crates::proconio::source::auto::AutoSource;use lazy_static::lazy_static;use std::io;use std::io::{BufReader,Stdin};use std::sync::Mutex;lazy_static!{#[doc(hidden)]pub static ref STDIN_SOURCE:Mutex<AutoSource<BufReader<Stdin>>>=Mutex::new(AutoSource::new(BufReader::new(io::stdin())));}#[macro_export]macro_rules!__cargo_equip_macro_def_proconio_input{(@from[$source:expr]@rest)=>{};(@from[$source:expr]@rest mut$($rest:tt)*)=>{$crate::__cargo_equip::crates::proconio::input!{@from[$source]@mut[mut]@rest$($rest)*}};(@from[$source:expr]@rest$($rest:tt)*)=>{$crate::__cargo_equip::crates::proconio::input!{@from[$source]@mut[]@rest$($rest)*}};(@from[$source:expr]@mut[$($mut:tt)?]@rest$var:tt:$($rest:tt)*)=>{$crate::__cargo_equip::crates::proconio::input!{@from[$source]@mut[$($mut)*]@var$var@kind[]@rest$($rest)*}};(@from[$source:expr]@mut[$($mut:tt)?]@var$var:tt@kind[$($kind:tt)*]@rest)=>{let$($mut)*$var=$crate::__cargo_equip::crates::proconio::read_value!(@source[$source]@kind[$($kind)*]);};(@from[$source:expr]@mut[$($mut:tt)?]@var$var:tt@kind[$($kind:tt)*]@rest,$($rest:tt)*)=>{$crate::__cargo_equip::crates::proconio::input!(@from[$source]@mut[$($mut)*]@var$var@kind[$($kind)*]@rest);$crate::__cargo_equip::crates::proconio::input!(@from[$source]@rest$($rest)*);};(@from[$source:expr]@mut[$($mut:tt)?]@var$var:tt@kind[$($kind:tt)*]@rest$tt:tt$($rest:tt)*)=>{$crate::__cargo_equip::crates::proconio::input!(@from[$source]@mut[$($mut)*]@var$var@kind[$($kind)*$tt]@rest$($rest)*);};(from$source:expr,$($rest:tt)*)=>{#[allow(unused_variables,unused_mut)]let mut s=$source;$crate::__cargo_equip::crates::proconio::input!{@from[&mut s]@rest$($rest)*}};($($rest:tt)*)=>{let mut locked_stdin=$crate::__cargo_equip::crates::proconio::STDIN_SOURCE.lock().expect(concat!("failed to lock the stdin; please re-run this program.  ","If this issue repeatedly occur, this is a bug in `proconio`.  ","Please report this issue from ","<https://github.com/statiolake/proconio-rs/issues>."));$crate::__cargo_equip::crates::proconio::input!{@from[&mut*locked_stdin]@rest$($rest)*}drop(locked_stdin);};}macro_rules!input{($($tt:tt)*)=>(crate::__cargo_equip_macro_def_proconio_input!{$($tt)*})}#[macro_export]macro_rules!__cargo_equip_macro_def_proconio_read_value{(@source[$source:expr]@kind[[$($kind:tt)*]])=>{$crate::__cargo_equip::crates::proconio::read_value!(@array@source[$source]@kind[]@rest$($kind)*)};(@array@source[$source:expr]@kind[$($kind:tt)*]@rest)=>{{let len=<usize as$crate::__cargo_equip::crates::proconio::source::Readable>::read($source);$crate::__cargo_equip::crates::proconio::read_value!(@source[$source]@kind[[$($kind)*;len]])}};(@array@source[$source:expr]@kind[$($kind:tt)*]@rest;$($rest:tt)*)=>{$crate::__cargo_equip::crates::proconio::read_value!(@array@source[$source]@kind[$($kind)*]@len[$($rest)*])};(@array@source[$source:expr]@kind[$($kind:tt)*]@rest$tt:tt$($rest:tt)*)=>{$crate::__cargo_equip::crates::proconio::read_value!(@array@source[$source]@kind[$($kind)*$tt]@rest$($rest)*)};(@array@source[$source:expr]@kind[$($kind:tt)*]@len[$($len:tt)*])=>{{let len=$($len)*;(0..len).map(|_|$crate::__cargo_equip::crates::proconio::read_value!(@source[$source]@kind[$($kind)*])).collect::<Vec<_>>()}};(@source[$source:expr]@kind[($($kinds:tt)*)])=>{$crate::__cargo_equip::crates::proconio::read_value!(@tuple@source[$source]@kinds[]@current[]@rest$($kinds)*)};(@tuple@source[$source:expr]@kinds[$([$($kind:tt)*])*]@current[]@rest)=>{($($crate::__cargo_equip::crates::proconio::read_value!(@source[$source]@kind[$($kind)*]),)*)};(@tuple@source[$source:expr]@kinds[$($kinds:tt)*]@current[$($curr:tt)*]@rest)=>{$crate::__cargo_equip::crates::proconio::read_value!(@tuple@source[$source]@kinds[$($kinds)*[$($curr)*]]@current[]@rest)};(@tuple@source[$source:expr]@kinds[$($kinds:tt)*]@current[$($curr:tt)*]@rest,$($rest:tt)*)=>{$crate::__cargo_equip::crates::proconio::read_value!(@tuple@source[$source]@kinds[$($kinds)*[$($curr)*]]@current[]@rest$($rest)*)};(@tuple@source[$source:expr]@kinds[$($kinds:tt)*]@current[$($curr:tt)*]@rest$tt:tt$($rest:tt)*)=>{$crate::__cargo_equip::crates::proconio::read_value!(@tuple@source[$source]@kinds[$($kinds)*]@current[$($curr)*$tt]@rest$($rest)*)};(@source[$source:expr]@kind[])=>{compile_error!(concat!("Reached unreachable statement while parsing macro input.  ","This is a bug in `proconio`.  ","Please report this issue from ","<https://github.com/statiolake/proconio-rs/issues>."));};(@source[$source:expr]@kind[$kind:ty])=>{<$kind as$crate::__cargo_equip::crates::proconio::source::Readable>::read($source)}}macro_rules!read_value{($($tt:tt)*)=>(crate::__cargo_equip_macro_def_proconio_read_value!{$($tt)*})}pub fn is_stdin_empty()->bool{use crate::__cargo_equip::crates::proconio::source::Source;let mut lock=STDIN_SOURCE.lock().expect(concat!("failed to lock the stdin; please re-run this program.  ","If this issue repeatedly occur, this is a bug in `proconio`.  ","Please report this issue from ","<https://github.com/statiolake/proconio-rs/issues>."));lock.is_empty()}}
        pub mod __proconio_derive_0_1_9 {pub use crate::__cargo_equip::macros::__proconio_derive_0_1_9::*;#[macro_export]macro_rules!__cargo_equip_macro_def___proconio_derive_0_1_9_derive_readable{($(_:tt)*)=>(::std::compile_error!("`derive_readable` from `proconio-derive 0.1.9` should have been expanded");)}#[macro_export]macro_rules!__cargo_equip_macro_def___proconio_derive_0_1_9_fastout{($(_:tt)*)=>(::std::compile_error!("`fastout` from `proconio-derive 0.1.9` should have been expanded");)}}
    }

    pub(crate) mod macros {
        pub mod __ac_library_rs_parted_internal_math_0_1_0 {}
        pub mod acl_modint {}
        pub mod __lazy_static_1_4_0 {pub use crate::{__cargo_equip_macro_def___lazy_static_1_4_0___lazy_static_create as __lazy_static_create,__cargo_equip_macro_def___lazy_static_1_4_0___lazy_static_internal as __lazy_static_internal,__cargo_equip_macro_def___lazy_static_1_4_0_lazy_static as lazy_static};}
        pub mod proconio {pub use crate::{__cargo_equip_macro_def_proconio_input as input,__cargo_equip_macro_def_proconio_read_value as read_value};}
        pub mod __proconio_derive_0_1_9 {pub use crate::{__cargo_equip_macro_def___proconio_derive_0_1_9_derive_readable as derive_readable,__cargo_equip_macro_def___proconio_derive_0_1_9_fastout as fastout};}
    }

    pub(crate) mod prelude {pub use crate::__cargo_equip::{crates::*,macros::__lazy_static_1_4_0::*};}

    mod preludes {
        pub mod __ac_library_rs_parted_internal_math_0_1_0 {}
        pub mod acl_modint {pub(in crate::__cargo_equip)use crate::__cargo_equip::crates::__ac_library_rs_parted_internal_math_0_1_0 as __acl_internal_math;}
        pub mod __lazy_static_1_4_0 {pub(in crate::__cargo_equip)use crate::__cargo_equip::macros::__lazy_static_1_4_0::*;}
        pub mod proconio {pub(in crate::__cargo_equip)use crate::__cargo_equip::macros::__lazy_static_1_4_0::*;pub(in crate::__cargo_equip)use crate::__cargo_equip::crates::{__lazy_static_1_4_0 as lazy_static,__proconio_derive_0_1_9 as proconio_derive};}
        pub mod __proconio_derive_0_1_9 {}
    }
}