#![allow(non_snake_case)] use crate::{modulo::StaticModInt, scanner::Scanner}; const M1: u64 = 754_974_721; const M2: u64 = 167_772_161; const M3: u64 = 469_762_049; modint!(M1); modint!(M2); modint!(M3); type Z1 = StaticModInt; type Z2 = StaticModInt; type Z3 = StaticModInt; fn main() { let mut scan = Scanner::new(); let a = scan.long(); let b = scan.long(); println!( "{}", if Z1::new(a).pow(b) == Z1::new(b).pow(a) && Z2::new(a).pow(b) == Z2::new(b).pow(a) && Z3::new(a).pow(b) == Z3::new(b).pow(a) { "Yes" } else { "No" } ); } pub mod scanner { use std::io::{stdin, BufReader, Bytes, Read, Stdin}; use std::str::FromStr; pub struct Scanner { buf: Bytes>, } impl Scanner { pub fn new() -> Scanner { Scanner { buf: BufReader::new(stdin()).bytes(), } } #[inline] fn token>(&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(&mut self) -> T { self.string().parse().ok().unwrap() } #[inline] pub fn string(&mut self) -> String { self.token() } #[inline] pub fn long(&mut self) -> i64 { self.read() } } } pub mod nums { use std::mem::swap; pub 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) } } pub mod modulo { use crate::nums::inv_gcd; 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::sync::atomic::{self, AtomicU32}; use std::thread::LocalKey; pub trait Modulus: 'static + PartialEq + Eq + Copy + Clone + std::hash::Hash + Ord { const M: u32; const HINT_M_IS_PRIME: bool; fn butterfly_cache() -> &'static LocalKey>>>; } pub trait DynamicModulus: 'static + PartialEq + Eq + Copy + Clone + std::hash::Hash + Ord { fn state() -> &'static AtomicU32 { static M: AtomicU32 = AtomicU32::new(1_000_000_007); &M } fn update(m: u32) { Self::state().store(m, atomic::Ordering::SeqCst) } fn umod() -> u32 { Self::state().load(atomic::Ordering::SeqCst) } } #[derive(PartialEq, Eq, Copy, Clone, Hash, PartialOrd, Ord)] pub enum DefaultId {} impl DynamicModulus for DefaultId {} macro_rules! impl_from_for_modint { ($name:ident, $guard: ident, $($tpe:ident),*) => { $( impl From<$tpe> for $name { fn from(n: $tpe) -> Self { Self::new(n) } } )* }; } macro_rules! impl_assign { ($name:ident, $guard:ident, $($t1:ty, $t2:ty, $fa:ident, $f:ident),*) => { $( impl $t1 for $name { type Output = Self; #[inline] fn $f(self, other: Self) -> Self { ::$f(self, other) } } impl $t2 for $name { #[inline] fn $fa(&mut self, other: Self) { *self = ::$f(*self, other); } } )* }; } macro_rules! impl_modint_structs { ($name:ident, $guard:ident) => { #[derive(PartialEq, Eq, Copy, Clone, Hash, PartialOrd, Ord)] #[repr(transparent)] pub struct $name { pub val: u32, phantom: PhantomData T>, } impl Debug for $name { fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result { self.val.fmt(f) } } impl $name { #[inline] pub fn new(a: U) -> Self { ::new(a) } #[inline] pub fn inv(self) -> Self { ::inv(self) } #[inline] pub fn raw(val: u32) -> Self { Self { val, phantom: PhantomData, } } #[inline] pub fn pow(self, x: U) -> Self { ::pow(self, x) } #[inline] pub fn zero() -> Self { ::zero() } #[inline] pub fn one() -> Self { ::one() } } impl std::fmt::Display for $name { fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result { write!(f, "{}", self.val) } } impl_from_for_modint!( $name, $guard, u8, u16, u32, u64, u128, i8, i16, i32, i64, i128, usize, isize ); impl_assign!( $name, $guard, Add, AddAssign, add_assign, add, Sub, SubAssign, sub_assign, sub, Mul, MulAssign, mul_assign, mul, Div, DivAssign, div_assign, div, Rem, RemAssign, rem_assign, rem ); impl Int for $name { impl_integer_functions!(|s: &Self| s.val, |x| Self::new(x), |s: &Self, n: i64| s .pow(n)); } }; } impl_modint_structs!(StaticModInt, Modulus); impl_modint_structs!(DynamicModInt, DynamicModulus); #[macro_export] macro_rules! modint { () => {$crate::modint!(1000000007, true);}; ($m:literal) => {$crate::modint!($m, true);}; ($m:literal, $is_prime:literal) => { $crate::modint!($m, ModValue, $is_prime); #[allow(dead_code)] type Z = $crate::modulo::StaticModInt; }; ($name:ident) => { $crate::modint!($name, $name, true); }; ($value:expr, $name:ident, $is_prime:literal) => { #[derive(Debug, PartialEq, Eq, Copy, Clone, Hash, PartialOrd, Ord)] pub enum $name {} impl $crate::modulo::Modulus for $name { const M: u32 = $value as _; const HINT_M_IS_PRIME: bool = $is_prime; fn butterfly_cache() -> &'static ::std::thread::LocalKey<::std::cell::RefCell<::std::option::Option<$crate::modulo::ButterflyCache>>> { thread_local! { static BUTTERFLY_CACHE: ::std::cell::RefCell<::std::option::Option<$crate::modulo::ButterflyCache<$name>>> = ::std::default::Default::default(); } &BUTTERFLY_CACHE } } }; } pub type D = DynamicModInt; pub trait ModInt: Int { fn new(val: U) -> Self { let x = val.to_i128(); Self::raw(x.rem_euclid(Self::modulus() as i128) as _) } fn inv(self) -> Self { if Self::mod_is_prime() { Self::pow(self, Self::modulus() - 2) } else { let (g, x) = inv_gcd(Self::val(self) as _, Self::modulus() as _); if g != 1 { panic!("the multiplicative inverse does not exist"); } else { Self::new(x) } } } fn raw(val: u32) -> Self; fn val(self) -> u32; fn modulus() -> u32; fn mod_is_prime() -> bool; fn add(self, other: Self) -> Self { let mut ret = self.val() + other.val(); if ret >= Self::modulus() { ret -= Self::modulus(); } Self::raw(ret) } fn sub(self, other: Self) -> Self { let mut ret = self.val().wrapping_sub(other.val()); if ret >= Self::modulus() { ret = ret.wrapping_add(Self::modulus()); } Self::raw(ret) } fn mul(self, other: Self) -> Self { Self::raw( (u64::from(self.val()) * u64::from(other.val()) % u64::from(Self::modulus())) as _, ) } fn div(self, other: Self) -> Self { self * other.inv() } fn rem(self, other: Self) -> Self { Self::raw(self.val() % other.val()) } fn pow(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 } } impl ModInt for StaticModInt { fn raw(val: u32) -> Self { Self::raw(val) } fn val(self) -> u32 { self.val } fn modulus() -> u32 { M::M } fn mod_is_prime() -> bool { M::HINT_M_IS_PRIME } } impl ModInt for DynamicModInt { fn raw(val: u32) -> Self { Self::raw(val) } fn val(self) -> u32 { self.val } fn modulus() -> u32 { M::umod() } fn mod_is_prime() -> bool { false } } pub struct ButterflyCache { pub sum_e: Vec>, pub sum_ie: Vec>, } } pub mod independent { pub mod integer { use std::fmt::Display; use std::ops::*; pub trait Int: Add + Sub + Mul + Div + Rem + 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() } fn powint(&self, n: i64) -> Self; } #[macro_export] macro_rules! impl_integer_functions { ($to_op:expr, $from_op:expr, $pow:expr) => { impl_integer_functions!( $to_op, $from_op, $pow, to_u8, from_u8, u8, to_u16, from_u16, u16, to_u32, from_u32, u32, to_u64, from_u64, u64, to_u128, from_u128, u128, to_i8, from_i8, i8, to_i16, from_i16, i16, to_i32, from_i32, i32, to_i64, from_i64, i64, to_i128, from_i128, i128, to_usize, from_usize, usize, to_isize, from_isize, isize ); }; ($to_op:expr, $from_op:expr, $pow: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 {$from_op(1)} fn powint(&self, n: i64) -> Self {$pow(self, n)} }; } macro_rules! impl_integer { ($($tpe:ident),*) => { $( impl Int for $tpe { impl_integer_functions!( |s: &Self| *s, |x| x as $tpe, |s: &Self, n: i64| s.pow(n as u32) ); } )* }; } impl_integer!(u8, u16, u32, u64, u128, i8, i16, i32, i64, i128, usize, isize); } }