How to create RSA PrivateKey from string with RSAPrivateKeySpec class in Java?

I have the below information and want to generate a public and private key in RSA (Java).

    String pubKey = "MFwwDQYJKoZIhvcNAQEBBQADSwAwSAJBAJXFRUWMDJZ+moC/VbcAXoY5dDxOruwI2B+B+YZRHSRRTKPyd9v0HTqdLeVgufLu/cSxlZAKtZDp9mfgyNdbY9ECAwEAAQ==";
    String privKey = "MIIBVAIBADANBgkqhkiG9w0BAQEFAASCAT4wggE6AgEAAkEAlcVFRYwMln6agL9VtwBehjl0PE6u7AjYH4H5hlEdJFFMo/J32/QdOp0t5WC58u79xLGVkAq1kOn2Z+DI11tj0QIDAQABAkBC1Bp71OkNAgL47edWWADVja9y9X0R70RYkst/hpQlTrjN4QxzN4k4gCqqdFkno2LfacRO7igMQuVEmYujfkbNAiEA/lU1CyW9J65FXSObsBLxqlNpFw79B2EKUkT6o7b2Ez8CIQCWwJlIyDaoXt7CrvTrPDpok7U93ZKmDPiRjjXDPsGU7wIhAJ6pITIXFO2QNg1ojVNGPiR3bHPKEedsjjfMeF9xYAmZAiAQnfpHg4pC1PJJE2/73g+yJ1X7E8ludE+R+9MBSpGcEQIgBWaVSyTx4e+gSulT93vnMpVsYmiwe53e5t4Uxs+cgSE=";
    String nModulusPublic = "AJXFRUWMDJZ-moC_VbcAXoY5dDxOruwI2B-B-YZRHSRRTKPyd9v0HTqdLeVgufLu_cSxlZAKtZDp9mfgyNdbY9E=";
    String eExponentPublic = "AQAB";
    String nModulusPrivate = "AJXFRUWMDJZ-moC_VbcAXoY5dDxOruwI2B-B-YZRHSRRTKPyd9v0HTqdLeVgufLu_cSxlZAKtZDp9mfgyNdbY9E=";
    String eExponentPrivate = "QtQae9TpDQIC-O3nVlgA1Y2vcvV9Ee9EWJLLf4aUJU64zeEMczeJOIAqqnRZJ6Ni32nETu4oDELlRJmLo35GzQ==";

These are main Encryption and decryption functions :

static String Decrypt(String encodedString,PrivateKey privKey) {
    try {
        Cipher cipher = Cipher.getInstance(cipherInstancename);
        cipher.init(Cipher.DECRYPT_MODE, privKey);
        byte[] decrypted = cipher.doFinal(Base64.getDecoder().decode(encodedString));
        return new String(decrypted, "UTF-8");
    } catch (Exception err) {
        return err.fillInStackTrace().toString();
    }
}

static String Encrypt(String encodedString,PublicKey pubKey) {
    try {
        Cipher cipher = Cipher.getInstance(cipherInstancename);
        cipher.init(Cipher.ENCRYPT_MODE, pubKey);
        byte[] plainBytes = new String(encodedString).getBytes("UTF-8");
        byte[] cipherData = cipher.doFinal(plainBytes);
        String encryptedString = Base64.getEncoder().encodeToString(cipherData);
        return encryptedString;
    } catch (Exception err) {
        return err.fillInStackTrace().toString();
    }
}

If I create PrivateKey and PublicKey with below function everything works great:

 static PrivateKey firstPrivateKey(String privateKeyStr) throws Exception {
    byte[] keyBytes = Base64.getDecoder().decode(privateKeyStr.getBytes(StandardCharsets.UTF_8));
    PKCS8EncodedKeySpec specPrivate = new PKCS8EncodedKeySpec(keyBytes);
    KeyFactory keyFactory = KeyFactory.getInstance("RSA");
    PrivateKey fileGeneratedPrivateKey = keyFactory.generatePrivate(specPrivate);
    RSAPrivateKey rsaPrv  = (RSAPrivateKey)(fileGeneratedPrivateKey);
    return  rsaPrv;
}
 static PublicKey firstPublicKey(String publicKeyStr) throws Exception {
    KeyFactory keyFactory = KeyFactory.getInstance("RSA");

    byte[] keyBytes = Base64.getDecoder().decode(publicKeyStr.getBytes(StandardCharsets.UTF_8));
    X509EncodedKeySpec specPublic = new X509EncodedKeySpec(keyBytes);
    PublicKey fileGeneratedPublicKey = keyFactory.generatePublic(specPublic);
    RSAPublicKey rsaPub  = (RSAPublicKey)(fileGeneratedPublicKey);
    return  rsaPub;
}

But I want to create them by this way with below function but decryption does not work:

 static PublicKey secondPublicKey(String publicKString,String publicExponentStr) throws Exception {
    byte[] modulusBytes = Base64.getDecoder().decode(publicKString);
    byte[] exponentBytes = Base64.getDecoder().decode(publicExponentStr);
    BigInteger modulus = new BigInteger(1, modulusBytes);
    BigInteger exponent = new BigInteger(1, exponentBytes);

    RSAPublicKeySpec rsaPubKey = new RSAPublicKeySpec(modulus, exponent);
    KeyFactory fact = KeyFactory.getInstance("RSA");
    PublicKey pubKey = fact.generatePublic(rsaPubKey);
    return pubKey;
}

static PrivateKey secondPrivateKey(String privateKString,String privateExponentStr) throws Exception {
    byte[] modulusBytes = Base64.getDecoder().decode(privateKString);
    byte[] exponentBytes = Base64.getDecoder().decode(privateExponentStr);
    BigInteger modulus = new BigInteger(1, modulusBytes);
    BigInteger exponent = new BigInteger(1, exponentBytes);

    RSAPrivateKeySpec privSpec = new RSAPrivateKeySpec(modulus,exponent);
    KeyFactory fact = KeyFactory.getInstance("RSA");
    PrivateKey privKey = fact.generatePrivate(privSpec);

    return privKey;
}

Using firstPrivateKey and firstPublicKey key generators and work nice:

   String a = Encrypt("test",firstPrivateKey(pubKey));
   String b = Decrypt(a, firstPublicKey(privKey));
   System.out.println(b);

Using second functions and does not work:

 String a = Encrypt("test",secondPublicKey(pubKey,eExponentPublic));
 String b = Decrypt(a, secondPrivateKey(privKey,eExponentPrivate));
 System.out.println(b);

What's the problem with secondPublicKey and secondPrivateKey functions?

Update:

I generate all keys and Modulus from this code, It seems my decoding is not ok:

    KeyPairGenerator kpg = KeyPairGenerator.getInstance("RSA");
    // RSAKeyGenParameterSpec spec = new RSAKeyGenParameterSpec(1024, RSAKeyGenParameterSpec.F4);
    kpg.initialize( 512 );
    KeyPair kp = kpg.generateKeyPair();
    String publicKeyStr = Base64.getEncoder().encodeToString(kp.getPublic().getEncoded());
    String privateKeyStr = Base64.getEncoder().encodeToString(kp.getPrivate().getEncoded());

    KeyFactory keyFactory = KeyFactory.getInstance("RSA");

    byte[] keyBytes = Base64.getDecoder().decode(publicKeyStr.getBytes(StandardCharsets.UTF_8));
    X509EncodedKeySpec specPublic = new X509EncodedKeySpec(keyBytes);
    PublicKey fileGeneratedPublicKey = keyFactory.generatePublic(specPublic);
    RSAPublicKey rsaPub  = (RSAPublicKey)(fileGeneratedPublicKey);

    keyBytes = Base64.getDecoder().decode(privateKeyStr.getBytes(StandardCharsets.UTF_8));
    PKCS8EncodedKeySpec specPrivate = new PKCS8EncodedKeySpec(keyBytes);
    PrivateKey fileGeneratedPrivateKey = keyFactory.generatePrivate(specPrivate);
    RSAPrivateKey rsaPrv  = (RSAPrivateKey)(fileGeneratedPrivateKey);


    BigInteger publicKeyModulus = rsaPub.getModulus();
    BigInteger publicKeyExponent  = rsaPub.getPublicExponent();
    BigInteger privateKeyModulus = rsaPrv.getModulus();
    BigInteger privateKeyExponent  = rsaPrv.getPrivateExponent();


    String nModulusPublic=Base64.getUrlEncoder().encodeToString(publicKeyModulus.toByteArray());
    String eExponentPublic=Base64.getUrlEncoder().encodeToString(publicKeyExponent.toByteArray());
    String nModulusPrivate=Base64.getUrlEncoder().encodeToString(privateKeyModulus.toByteArray());
    String eExponentPrivate=Base64.getUrlEncoder().encodeToString(privateKeyExponent.toByteArray());

    System.out.println(publicKeyStr);
    System.out.println(privateKeyStr);
    System.out.println( nModulusPublic);
    System.out.println(eExponentPublic);
    System.out.println( nModulusPrivate);
    System.out.println(eExponentPrivate);