def main():
    # Affine cipher: E(x) = (ax + b) mod 26
    # Given: "ab" -> "GL"
    # a=0, b=1 -> G=6, L=11
    # So: 6 = (a*0 + b) mod 26 -> b = 6
    # And: 11 = (a*1 + b) mod 26 -> 11 = (a + 6) mod 26 -> a = 5

    ciphertext = "XPALASXYFGFUKPXUSOGEUTKCDGEXANMGNVS"

    # Try all possible values of a and b for affine cipher
    for a in range(1, 26):
        # a must be coprime to 26
        if gcd(a, 26) != 1:
            continue

        for b in range(26):
            # Check if this key produces "ab" -> "GL"
            if (a * 0 + b) % 26 == 6 and (a * 1 + b) % 26 == 11:
                # Found the key, now decrypt the message
                a_inv = mod_inverse(a, 26)
                decrypted = ""
                for char in ciphertext:
                    if char.isalpha():
                        y = ord(char.upper()) - ord('A')
                        x = (a_inv * (y - b)) % 26
                        decrypted += chr(x + ord('A'))
                    else:
                        decrypted += char

                print(f"Key found: a={a}, b={b}")
                print(f"Ciphertext: {ciphertext}")
                print(f"Decrypted: {decrypted}")
                return

def gcd(a, b):
    while b:
        a, b = b, a % b
    return a

def mod_inverse(a, m):
    for i in range(1, m):
        if (a * i) % m == 1:
            return i
    return None

if __name__ == '__main__':
    main()