import sys import math MOD = 998244353 def main(): N, M = map(int, sys.stdin.readline().split()) max_n = N fact = [1] * (max_n + 1) for i in range(1, max_n + 1): fact[i] = fact[i-1] * i % MOD inv_fact = [1] * (max_n + 1) inv_fact[max_n] = pow(fact[max_n], MOD-2, MOD) for i in range(max_n-1, -1, -1): inv_fact[i] = inv_fact[i+1] * (i+1) % MOD inv_2 = pow(2, MOD-2, MOD) inv_2_pows = pow(inv_2, 2*N, MOD) def comb(n, k): if k < 0 or k > n: return 0 return fact[n] * inv_fact[k] % MOD * inv_fact[n - k] % MOD def get_divisors(m): divisors = set() if m == 0: return divisors m_abs = abs(m) for i in range(1, int(math.isqrt(m_abs)) + 1): if m_abs % i == 0: divisors.add(i) divisors.add(m_abs // i) divisors.add(m_abs) res = set() for d in divisors: res.add(d) res.add(-d) return res answer = 0 if M == 0: for a in range(N+1): b = N - a sum_x_sq = 0 sum_y_sq = 0 for s in range(-a, a+1, 2): cnt_x = comb(a, (a + s) // 2) if cnt_x == 0: continue for t in [-s, s]: if abs(t) > b or (b - t) % 2 != 0: continue cnt_y = comb(b, (b + t) // 2) if cnt_y == 0: continue term = comb(N, a) term = term * cnt_x % MOD term = term * cnt_y % MOD term = term * inv_2_pows % MOD answer = (answer + term) % MOD print(answer) return divisors = get_divisors(M) required_parity = N % 2 for A in divisors: B = M // A if (A % 2 != required_parity) or (B % 2 != required_parity): continue X = (A + B) // 2 Y = (B - A) // 2 if (A + B) % 2 != 0 or (B - A) % 2 != 0: continue abs_X = abs(X) abs_Y = abs(Y) min_a = abs_X max_a = N - abs_Y if min_a > max_a: continue a_parity = X % 2 start_a = min_a if (min_a % 2 == a_parity) else (min_a + 1) if start_a > max_a: continue num_steps = (max_a - start_a) // 2 + 1 for k in range(num_steps): a = start_a + 2 * k b_val = N - a if b_val < abs_Y: continue if (b_val % 2) != (Y % 2): continue c_n_a = comb(N, a) if c_n_a == 0: continue x = X y = Y c_a = comb(a, (a + x) // 2) c_b = comb(b_val, (b_val + y) // 2) if c_a == 0 or c_b == 0: continue term = c_n_a * c_a % MOD term = term * c_b % MOD term = term * inv_2_pows % MOD answer = (answer + term) % MOD print(answer % MOD) if __name__ == '__main__': main()