Given positive integers from $1$ to $N$ where $N$ can go upto $10^9$. Some $K$ integers from these given integers are missing. $K$ can be at max $10^5$ elements. I need to find the minimum sum that can't be formed from remaining $N-K$ elements in an efficient way.
Example; say we have $N=5$ it means we have ${(1,2,3,4,5)}$ and let $K=2$ and missing elements are: ${(3,5)}$ then remaining array is now ${(1,2,4)}$ the minimum sum that can't be formed from these remaining elements is 8 because :
$1=1$
$2=2$
$3=1+2$
$4=4$
$5=1+4$
$6=2+4$
$7=1+2+4$
So how to find this un-summable minimum?
I did find a link but that is the reverse of this problem :-
https://stackoverflow.com/questions/21060873/minimum-sum-that-cant-be-obtained-from-a-set
There are a few dirty cases that can directly check say if 1 is missing then 1 cannot be formed similarly if 2 is missing then 2 cannot be formed