public class Crypto {
// Given y != 0, yield x mod y: the value r such that
// x = q*y + r  and 0 <= r < abs(y) (for some q)
public static long mod(long x, long y) {
    // q*y + r  =  (-q)*(-y) + r ,
    // so r depends only on abs(y)
    y= Math.abs(y);

    // For x >= 0 and y > 0, mod(x,y) = x % y
    // For x <  0 and y > 0, x % y is the value r that
    // satisfies x = q*y + r and y < r <= 0.
    long r= x % y;
    if (r >= 0) return r;
    return y+r;
    }
    
// Given a>=0, b>0, yield a**b
public static long exp(long a, long b) {
    long z= 1;
    long x= a;
    long y= b;
    // invariant a**b = z*x**y  and y >= 0
    while (y > 0) {
        if (y % 2 == 0)
            {x= x*x; y= y/2;}
        else{z= z*x; y= y-1;}
        }
    return z;
    }
    
// Given 0<=a<m, 0<b<m, yield a**b using modulo m arithmetic
public static long expMod(long a, long b, long m) {
    
    }
    
// Yield a long array of size s.length(): element i of
// the array should be the encryption of character
// s.charAt[i], using a public key that consists of key k
// and modulus m.
public static long[] encrypt(String s, long k, long m) {
        
    }
        
// Yield a String of size c.length(): element i of the
// String should be the decryption of the integer c[i],
// using a private key that consists of key k and modulus m.
public static String decrypt(long[] c, long k, long m) {
    String s= "";
    int i= 0;
    // invariant: s[0..i-1] contains the decrypted versions
    //            of c[0..i-1]
    while (i != c.length) {
        s= s + (char)expMod(c[i], k, m); 
        i= i+1;
        }
    return s;
    }
    
// Yield an array c (say) of size s.length() that is
// the "fancy" encryption of String s. The definition of
// c is as follows, with all arithmetic being modulo m. First,
//     c[0] = expMod(s[0],k,m).
// Then, for i in 1..s.length()-1,
//     c[i] = expMod(s[s_i] + c[i-1],k,m)
public static long[] fancyEncrypt(String s, long k, long m) {
        
    }
        
// Yield the fancy-decryption of array c, i.e. the String s
// such that fancyEncrypt(s,k,m) produced c. 
public static String fancyDecrypt(long[] c, long k, long m) {
        
    }
 
}