Minimum Subsegment Length

You are given an array of n positive integers and a target sum S. Your task is to find the minimum length of a contiguous subarray (subsegment) such that the sum of the subarray is greater than or equal to S. If no such subarray exists, output -1.

Formally, given an array a of numbers, find the smallest integer k such that there exists an index i satisfying

$$\sum_{j=i}^{i+k-1} a_j \ge S$$

If no valid subsegment exists, print -1.

Example: For n = 8, S = 15, and a = [1, 2, 3, 4, 5, 6, 7, 8], the minimum valid subsegment is [7,8] whose length is 2.

inputFormat

The first line of input contains two integers n and S separated by a space, where n is the number of elements in the array and S is the target sum.

The second line contains n positive integers separated by spaces representing the elements of the array.

outputFormat

Output a single integer, the minimum length of a contiguous subarray whose sum is greater than or equal to S. If no such subarray exists, output -1.

## sample

8 15
1 2 3 4 5 6 7 8

2

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