#using ChatGPT o1-preview mod = 998244353 def linear_sieve(N): mu = [1] * (N + 1) spf = [0] * (N + 1) # 最小素因数 primes = [] for i in range(2, N + 1): if spf[i] == 0: spf[i] = i mu[i] = -1 primes.append(i) for p in primes: if p * i > N: break spf[p * i] = p if i % p == 0: mu[p * i] = 0 break else: mu[p * i] = -mu[i] return mu, spf def factorize(n, spf): factors = {} while n > 1: p = spf[n] factors[p] = factors.get(p, 0) + 1 n //= p return factors def generate_divisors(factors): from itertools import product exponents_list = [] for p, exp in factors.items(): exponents_list.append([p ** e for e in range(exp + 1)]) divisors = set() for exponents in product(*exponents_list): prod = 1 for e in exponents: prod *= e divisors.add(prod) return list(divisors) def main(): def solve(): K_str, N_str = input().split() K = int(K_str) N = int(N_str) mod = 998244353 if N == 1: if K == 1: print(2) else: print(3) return mu, spf = linear_sieve(N) factors = factorize(N, spf) divisors = generate_divisors(factors) total = 0 for d in divisors: nd = N // d mu_nd = mu[nd] if mu_nd == 0: continue pow2d = pow(2, d, mod) total = (total + mu_nd * pow2d) % mod total = (total + mod) % mod # 負の値を回避 print(total) solve() main()