Important scientific number (Editorial)

We know that:

• a + x is divisible by $b$;

• b + x is divisible by $a$;

Therefore, a + b + x is divisible by both $a$ and $b$, which is equivalent to its divisibility by LCM(a, b). That is, there exists an integer $k$ such that:

We take x = LCM(a, b) - a - b as the solution. However, if this value is negative, we instead use:

It is evident that a + b \le 2 \cdot LCM(a, b).

Example

In the second example a = 3, b = 4.~LCM(3, 4) = 12.

The answer is x = LCM(a, b) - a - b = 12 - 3 - 4 = 5.

In the third example a = 123, b = 123. LCM(123, 123) = 123.

The answer is x = LCM(a, b) - a - b = 123 - 123 - 123 = -123. Since this value is negative, the answer is

Algorithm implementation

The function gcd computes the greatest common divisor of the numbers $a$ and $b$.

long long gcd(long long a, long long b)
{
  return (!b) ? a : gcd(b, a % b);
}

Read the input data.

cin >> a >> b;

Compute lcm = LCM(a, b) = (a \cdot b)~/~GCD(a, b).

lcm = a / gcd(a, b) * b;

Compute the answer.

res = lcm - a - b;
if (res < 0) res += lcm;

Print the answer.

cout << res << endl;