[17NOIP Improvement Team] T2 Xiaokai’s doubts

P3951 Xiaokai's doubts

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Idea:
If a<b,
suppose x is the answer:
$$x=ma+nb$$
Obviously, n>=0, x will definitely be expressed, which does not meet the meaning of
thequestion. Then suppose n=-1, then x=ma-b is
the largest that cannot be expressed. So, is it enough to make m the largest?
Let's discuss it in three situations:

1. m=b, bring it into the original formula:
   $$x=ma-b$$
   $$Get:x=ba-b$$
   $$I.e.x=(a-1)b$$
   then n is not greater than 0, which does not meet the meaning of the question

2. m>b, suppose m=b+1;
   bring back to the original formula: (b+1)ab
   ad+ab
   (a-1)b+a
   bring back ma+nb, you will find that n=a-1, then this It's not a positive number anymore, it doesn't meet the meaning of the question.

3. m<b, then the maximum is b-1
   brought back to the original formula: (b-1)ab
   and then you will find that this is not enough.
   So simplify again:
   Answer: ab-ab

#include<bits/stdc++.h>
long long a,b;
int main()
{
    
    
    scanf("%lld%lld",&a,&b);
    printf("%lld\n",(a*b-a-b);
    return 0;
}