Smallest Integer Not Representable as Subset Sum

Given a non-decreasing sorted array ARR of N positive numbers, determine the smallest positive integer that cannot be expressed as the sum of elements from any proper subset of the array.

Example:

Input:

ARR = [1, 1, 3]

Output:

6

Explanation:

The possible sums of subsets are:
1 → [1] 
2 → [1, 1]
3 → [3]
4 → [1, 3]
5 → [1, 1, 3]
The smallest integer not representable as a subset sum is 6.

Constraints:

• 1 <= T <= 100
• 1 <= N <= 10^4
• 0 <= arr[i] <= 10^9