[Luogu] 小凯的疑惑

https://www.luogu.org/problemnew/show/P3951

考场上打表找规律的我写出了这样一份代码(紧张到爆<已经爆>)

当时一出考场听说是O(1)做法，当时就懵了(唉)

#include <iostream>
#include <cstdio>
#include <algorithm>
 
using namespace std;
 
#define LL long long
#define gc getchar()
 
LL a, b, imp;
 
inline LL read() {
    LL x = ;
    char c = gc;
    while(c < '' || c > '') c = gc;
    while(c >= '' && c <= '') x = x *  + c - '', c = gc;
    return x;
}
 
LL gcd(LL aa, LL bb) {
    return bb ==  ? aa : gcd(bb, aa % bb);
}
 
int main() {
    a = read();
    b = read();
    if(a < b) swap(a, b);
    for(int i = b; ; i --) {
        if(gcd(i, b) == ) {
            printf("%lld", i * a - b);
            return ;
        }
    }
 
    return ;
}

Answer = a * b - a - b;