import java.math.BigInteger;

class HelloWorld {
    public static void main(String[] args) {


      BigInteger one = new BigInteger("1");
      BigInteger two = new BigInteger ("2");
      BigInteger four = new BigInteger("4");

      BigInteger n = new BigInteger("837210799");
      BigInteger e = new BigInteger("7");
      BigInteger e_2 = new BigInteger("17");
      BigInteger d = new BigInteger("478341751");

      BigInteger k = d.multiply(e).subtract(one).divide(n).add(BigInteger.ONE);

      System.out.println("k is "+k);
      BigInteger p_plus_q = k.multiply(n.add(one)).add(one).subtract(e.multiply(d)).divide(k);
      System.out.println("P+q is "+p_plus_q);
   BigInteger delta = p_plus_q.multiply(p_plus_q).subtract(four.multiply(n));

     System.out.println("delta is "+delta);


      BigInteger p =p_plus_q.add(sqrt(delta)).divide(two);
      BigInteger q = p_plus_q.subtract(sqrt(delta)).divide(two);
      System.out.println("P is "+p);
      System.out.println("Q is "+q);


     BigInteger d_2 =e_2.modInverse(p.subtract(one).multiply(q.subtract(one)));

      System.out.println("The second private key is "+d_2);



    }

    public static BigInteger sqrt(BigInteger n) {
    BigInteger a = BigInteger.ONE;
    BigInteger b = n.shiftRight(5).add(BigInteger.valueOf(8));
    while (b.compareTo(a) >= 0) {
        BigInteger mid = a.add(b).shiftRight(1);
        if (mid.multiply(mid).compareTo(n) > 0) {
            b = mid.subtract(BigInteger.ONE);
        } else {
            a = mid.add(BigInteger.ONE);
        }
    }
    return a.subtract(BigInteger.ONE);
}

}