// -*- coding:utf-8-unix -*- // #![feature(map_first_last)] #![allow(dead_code)] #![allow(unused_imports)] #![allow(unused_macros)] // use core::num; use std::cmp::*; use std::fmt::*; use std::hash::*; use std::iter::FromIterator; use std::*; use std::{cmp, collections, fmt, io, iter, ops, str}; const INF: i64 = 1223372036854775807; const UINF: usize = INF as usize; const LINF: i64 = 2147483647; const INF128: i128 = 1223372036854775807000000000000; const MOD1: i64 = 1000000007; const MOD9: i64 = 998244353; const MOD: i64 = MOD9; // const MOD: i64 = MOD2; const UMOD: usize = MOD as usize; const M_PI: f64 = 3.14159265358979323846; // use proconio::input; // const MOD: i64 = INF; use cmp::Ordering::*; use std::collections::*; use std::io::stdin; use std::io::stdout; use std::io::Write; macro_rules! p { ($x:expr) => { //if expr println!("{}", $x); }; } macro_rules! vp { // vector print separate with space ($x:expr) => { println!( "{}", $x.iter() .map(|x| x.to_string()) .collect::>() .join(" ") ); }; } macro_rules! d { ($x:expr) => { eprintln!("{:?}", $x); }; } macro_rules! yn { ($val:expr) => { if $val { println!("Yes"); } else { println!("No"); } }; } macro_rules! map{ // declear btreemap ($($key:expr => $val:expr),*) => { { let mut map = ::std::collections::BTreeMap::new(); $( map.insert($key, $val); )* map } }; } macro_rules! set{ // declear btreemap ($($key:expr),*) => { { let mut set = ::std::collections::BTreeSet::new(); $( set.insert($key); )* set } }; } fn main() { solve(); } // use str::Chars; #[allow(dead_code)] fn read() -> T { let mut s = String::new(); std::io::stdin().read_line(&mut s).ok(); s.trim().parse().ok().unwrap() } #[allow(dead_code)] fn read_vec() -> Vec { read::() .split_whitespace() .map(|e| e.parse().ok().unwrap()) .collect() } #[allow(dead_code)] fn read_mat(n: u32) -> Vec> { (0..n).map(|_| read_vec()).collect() } #[allow(dead_code)] fn readii() -> (i64, i64) { let mut vec: Vec = read_vec(); (vec[0], vec[1]) } #[allow(dead_code)] fn readiii() -> (i64, i64, i64) { let mut vec: Vec = read_vec(); (vec[0], vec[1], vec[2]) } #[allow(dead_code)] fn readuu() -> (usize, usize) { let mut vec: Vec = read_vec(); (vec[0], vec[1]) } #[allow(dead_code)] fn readff() -> (f64, f64) { let mut vec: Vec = read_vec(); (vec[0], vec[1]) } fn readcc() -> (char, char) { let mut vec: Vec = read_vec(); (vec[0], vec[1]) } fn readuuu() -> (usize, usize, usize) { let mut vec: Vec = read_vec(); (vec[0], vec[1], vec[2]) } #[allow(dead_code)] fn readiiii() -> (i64, i64, i64, i64) { let mut vec: Vec = read_vec(); (vec[0], vec[1], vec[2], vec[3]) } #[allow(dead_code)] fn readuuuu() -> (usize, usize, usize, usize) { let mut vec: Vec = read_vec(); (vec[0], vec[1], vec[2], vec[3]) } fn read_imat(h: usize) -> Vec> { (0..h).map(|_| read_vec()).collect() } fn read_cmat(h: usize) -> Vec> { (0..h).map(|_| read::().chars().collect()).collect() } fn prime_factorization(x: usize) -> BTreeMap { let mut res: BTreeMap = BTreeMap::new(); let mut xx = x; let mut p: usize = 2; while p * p <= xx { while xx % p == 0 { // println!("{:?}", p); let t = res.get_mut(&p); if t.is_none() { res.insert(p, 1); } else { *t.unwrap() += 1; } xx /= p; } // println!("{:?} {:?}", p, res); p += 1; } if xx != 1 { let t = res.get_mut(&xx); if t.is_none() { res.insert(xx, 1); } else { *t.unwrap() += 1; } } res } pub struct Montgomery { m: usize, pow_r: usize, mp: usize, mask: usize, r2: usize, } impl Montgomery { pub fn new(m: usize, pow_r: usize) -> Self { fn extended_gcd(a: i128, b: i128) -> (i128, i128) { if (a, b) == (1, 0) { (1, 0) } else { let (x, y) = extended_gcd(b, a % b); (y, x - (a / b) * y) } } let mp = { let (_, b) = extended_gcd(1i128 << pow_r, m as i128); if b <= 0 { (-b) as usize } else { (-b + (1 << pow_r)) as usize } }; let mask = std::usize::MAX; let r2 = (((1u128 << pow_r) % m as u128) * ((1u128 << pow_r) % m as u128) % m as u128) as usize; Montgomery { m, pow_r, mp, mask, r2, } } /// - Returns: /// - t * R^{-1} mod N fn mr(&self, t: u128) -> usize { let temp = { let mask = self.mask as u128; let mp = self.mp as u128; let m = self.m as u128; let pow_r = self.pow_r as u128; ((t + ((t & mask) * mp & mask) * m) >> pow_r) as usize }; if temp >= self.m { temp - self.m } else { temp } } /// - Returns: /// - a + b mod N pub fn add(&self, a: usize, b: usize) -> usize { (a + b) % self.m } /// - Returns: /// - a * b mod N pub fn mul(&self, a: usize, b: usize) -> usize { self.mr(self.mr(a as u128 * b as u128) as u128 * self.r2 as u128) } } /// - Returns: /// - GCD(a, b) pub fn gcd(mut a: usize, mut b: usize) -> usize { if a < b { std::mem::swap(&mut a, &mut b); } while b != 0 { let temp = a % b; a = b; b = temp; } a } /// - Returns: /// - if n is prime number: /// * true /// - else: /// * false /// /// - Note: /// - Algorithm: /// - Miller-Rabin pub fn is_prime_large(n: usize) -> bool { if n == 0 || n == 1 || (n > 2 && n % 2 == 0) { return false; } if n == 2 { return true; } /// - Returns: /// - $a^{n}$ modulo $m$ pub fn mod_pow(a: usize, mut n: usize, mont: &Montgomery) -> usize { let mut res = 1; let mut x = a; while n > 0 { if n % 2 == 1 { res = mont.mul(res, x); } x = mont.mul(x, x); n /= 2; } res } let s = (n - 1).trailing_zeros(); let d = (n - 1) / (1 << s); let mont = Montgomery::new(n, 64); let f = |mut a| { a %= n; if a == 0 { return true; } let mut ad = mod_pow(a, d, &mont); if ad == 1 || ad == n - 1 { return true; } for _ in 0..s { ad = mont.mul(ad, ad); if ad == n - 1 { return true; } } false }; const A: [usize; 7] = [2, 325, 9375, 28178, 450775, 9780504, 1795265022]; A.iter().all(|x| f(*x)) } pub fn factorize_sub(n: usize, res: &mut Vec) { if n == 1 { return; } if is_prime_large(n) { res.push(n); return; } let n2 = (n as f64).powf(1.0 / 8.0) as usize; // find divisor of n let d = if n % 2 == 0 { 2 } else { (|| { let mont = Montgomery::new(n, 64); for c in 1234567891.. { let f = |a, mont: &Montgomery| mont.add(mont.mul(a, a), c); let mut a = vec![2, f(2, &mont)]; let mut i1 = 0; let mut i2 = 1; loop { let mut q = 1; for _ in 0..n2 { a.push(f(a[i2], &mont)); a.push(f(a[i2 + 1], &mont)); i1 += 1; i2 += 2; q = mont.mul(q, std::cmp::max(a[i1], a[i2]) - std::cmp::min(a[i1], a[i2])); } let g = gcd(q, n); if 1 < g && g < n { return g; } if g == n { break; } a.push(f(a[i2], &mont)); a.push(f(a[i2 + 1], &mont)); i1 += 1; i2 += 2; } let mut a = vec![2, f(2, &mont)]; let mut i1 = 0; let mut i2 = 1; loop { let g = gcd(std::cmp::max(a[i1], a[i2]) - std::cmp::min(a[i1], a[i2]), n); if 1 < g && g < n { return g; } if g == n { break; } a.push(f(a[i2], &mont)); a.push(f(a[i2 + 1], &mont)); i1 += 1; i2 += 2; } } unreachable!() })() }; factorize_sub(d, res); factorize_sub(n / d, res); } /// - Returns: /// - result of integer factorization of n /// - Note: /// - Algorithm: /// - Pollard's rho algorithm pub fn factorize(n: usize) -> Vec { assert!(n != 0); let mut res = vec![]; factorize_sub(n, &mut res); res.sort(); res } fn solve() { let (n, k) = readuu(); let factors = factorize(k); let mut pf = map![]; for f in factors { let t = pf.get(&f); if t.is_none() { pf.insert(f, 1); } else { pf.insert(f, t.unwrap() + 1); } } let mut max_divise_num = map![]; let mut vec: Vec = read_vec(); // let primes = pf.keys().collect::>(); let mut primes: Vec = vec![]; for (k, _) in &pf { primes.push(*k); } for i in 0..n { let mut x = vec[i]; for p in &primes { let mut cnt = 0; while x % p == 0 { x /= p; cnt += 1; } let t = max_divise_num.get_mut(p).copied(); if t.is_none() { max_divise_num.insert(*p, cnt); } else { max_divise_num.insert(*p, max(cnt, t.unwrap())); } } } let mut can_divise = true; for (k, v) in &pf { let num = max_divise_num.get(k).copied().unwrap_or(0); if num < *v { can_divise = false; break; } } yn!(can_divise); return; }