i have two arrays ,each of size n, which are sorted.

write an algorithm that finds the k'th smallest amongst the "sum" of the two arrays

in O(lg min (k,2n-k))

i have this idea of how to solve it.

in the added picture

i find the k smallest of array A by A[k] and k smallest of array B by B[k]

and the k smallest of the sum is between those

in my photo k2>k1

i wrote the following function but i dont know how to know if i got the k'th smallest in the recurtion.and i am not sure abiut the sub arrays ranges in the recursive calls

Mikum(A,q,r)

k1=A[k/2]

k2=B[k/2]

If (x>y)

Mikum(A,k, n)

Mikum(B,0 ,k)