import base64
from cryptography.hazmat.primitives import serialization
from cryptography.hazmat.primitives.asymmetric import rsa

# The XML data provided by the user
modulus_b64 = "3PlhZKih1S9AKmsOcnPuS6FfPyYdKg6ltCUypt4EOi2++oM5O26YFxODBtQHO+UmsEoNcz6X2A5BE9kv4y8Xyv+hDxQrHsyavrkq2Yn5Mf/BFAquYuRoX5FtvH6ht+yllfBJQs3wE9m/O8LKHomKE5HXiaV/QMDRLoYeAwzQwcE="
exponent_b64 = "AQAB"
d_b64 = "i8TdWprjSgHKF0qB59j2WDYpFbtY5RpAq3J/2FZD3DzFOJU55SKt5qK71NzV+oeV8hnU6hkkWE+j0BcnGA7Yf6xGIoVNVhrenU18hrd6vSUPDeOuerkv+u98pNEqs6jcfYwhKKEJ2nFl4AacdQ7RaQPEWb41pVYvP+qaX6PeQAE="
p_b64 = "8fGRi846fRCbc8oaUGnw1dR2BXOopzxfAMeKEOCUeRP/Yj1kUcW9k4zUeaFc2upnfAeUbX38Bk5VW5edCDIjAQ=="
q_b64 = "6c/usvg8/4quH8Z70tSotmN+N6UxiuaTF51oOeTnIVUjXMqB3gc5sRCbipGj1u+DJUYh4LQLZp+W2LU7uCpewQ=="
dp_b64 = "y2q8YVwh5tbYrHCm0SdRWqcIF6tXiEwE4EXkOi5oBqielr1hJDNqIa1NU3os9M4R9cD1tV0wUSj5MUn2uFZXAQ=="
dq_b64 = "yc9+8Z0QUWVrC+QvBngls1/HFtKQI5sHRS/JQYdQ9FVfM31bgL/tzOZPytgQebm8EdUp8qCU4pxHAH/Vrw1rQQ=="
inverse_q_b64 = "VX4SRxVQ130enAqw9M0Nyl+875vmhc6cbsJQQ3E/fJjQvkB8EgjxBp6JVTeY1U5ga56Hvzngomk335pA6gli0A=="

def b64_to_int(b64_str):
    return int.from_bytes(base64.b64decode(b64_str), byteorder='big')

# Convert components to integers
n = b64_to_int(modulus_b64)
e = b64_to_int(exponent_b64)
d = b64_to_int(d_b64)
p = b64_to_int(p_b64)
q = b64_to_int(q_b64)
dmp1 = b64_to_int(dp_b64)
dmq1 = b64_to_int(dq_b64)
iqmp = b64_to_int(inverse_q_b64)

# Reconstruct the private key object
private_key = rsa.RSAPrivateNumbers(
    p=p,
    q=q,
    d=d,
    dmp1=dmp1,
    dmq1=dmq1,
    iqmp=iqmp,
    public_numbers=rsa.RSAPublicNumbers(e, n)
).private_key()

# Serialize to PEM
pem_private = private_key.private_bytes(
    encoding=serialization.Encoding.PEM,
    format=serialization.PrivateFormat.PKCS8,
    encryption_algorithm=serialization.NoEncryption()
)

# Print for the user
print(pem_private.decode('utf-8'))