Minimum Size Subarray Sum

Given an array a of n integers and an integer x, determine the minimal length of a contiguous subarray such that the sum of its elements is greater than or equal to x. If no such subarray exists, output -1.

Mathematical formulation:

Find the smallest integer l such that there exists an index i with \[ \sum_{j=i}^{i+l-1} a_j \ge x \] If no valid subarray exists then return -1.

The problem is best approached using a sliding window technique.

inputFormat

The input is given via standard input (stdin) in the following format:

1. The first line contains an integer n denoting the length of the array.
2. The second line contains n space-separated integers representing the array a.
3. The third line contains an integer x.

outputFormat

Output to standard output (stdout) a single integer: the minimal length of a contiguous subarray of a whose sum is at least x. If no valid subarray exists, output -1.

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