1. (20%) Consider an RSA cryptographic system with the public key \( (n, e) = (649, 387) \). First, find prime numbers \( p \) and \( q \) such that \( n = pq \). Second, find the value of \( d \) in the private key \( (n, d) \). Third, decrypt the ciphertext 10 into plaintext. Fourth, encrypt the plaintext 351 into ciphertext. Finally, answer the question "Is it possible to find more than one values of \( d \) in the range \( 0 < d < (p - 1)(q - 1) \) that works in decryption?" If your answer is YES, find all possible values of \( d \); if your answer is NO, give a brief proof.