 Distinct-index two-sum by suffix lower bounds

For each candidate first index $i$ in a sorted array, use lower-bound search for $t-a(i)$ only in the suffix starting at $i+1$. A matching result is automatically at a different position. The outer loop invariant excludes all solutions whose smaller index precedes $i$; an unsuccessful suffix search extends this exclusion by one. Exhaustion proves absence of any pair. Searching all suffixes gives $O(N\log (N+1))$ running time and constant auxiliary space. Compute the complement in a sufficiently wide type to avoid integer overflow before comparison.