Zero Sum Subarray

Given an array of integers and an integer k, determine whether there exists a contiguous subarray of length at least k whose sum equals zero.

A subarray is defined as a contiguous portion of the array.

Constraints:

• $$1 \le n \le 1000$$, where n is the number of elements in the array.
• $$-10^4 \le nums[i] \le 10^4$$ for each element nums[i].
• $$1 \le k \le n$$

Example:

Input:
7
1 2 -3 4 -2 -2 5
3
Output:
True

</p>

inputFormat

The input is read from stdin and consists of three lines:

1. The first line contains a single integer n, the number of elements in the array.
2. The second line contains n space-separated integers representing the array elements.
3. The third line contains a single integer k.

outputFormat

Print to stdout a single line containing either True if there exists a contiguous subarray of length at least k that sums to zero, or False otherwise.

## sample

7
1 2 -3 4 -2 -2 5
3

True