AndyMan68 is back yet again with another sliding window problem! This time, he imagines a window of size ~W~, sliding from the leftmost position in an array to the rightmost. He wants to ensure each window's elements sum to at least ~K~. However, large windows are expensive! He wants to find the minimum window size such that this condition is met.

Formally, he wants to find the minimum value ~W~ such that all subarrays of size ~W~ have a sum of ~K~ or greater.

Help AndyMan68 solve this problem!

Input Specification

The first line contains two spaced integers ~N~ ~(1 \le N \le 10^5)~ and ~K~ ~(1 \le K \le \text{sum} (a_i))~, representing the number of elements in the array and the minimum sum required for the sliding window.

The next line contains ~N~ spaced integers, where the ~i^{\text{th}}~ integer is ~a_i~ ~(0 \le a_i \le 10^5)~.

Output Specification

On a single line, output the minimum window size ~W~ required such that all windows of size ~W~ has a sum of at least ~K~. You may assume that the minimum ~W~ will be greater than ~0~ and less than or equal to ~N~.

Beware of integer overflow as the sum within a window can exceed the integer limit in some languages such as C++.

Sample Input 1

5 7
2 9 3 2 4

Output for Sample Input 1

3

Explanation of Output for Sample Input 1

The windows of size ~3~ can be seem below:

~[2 \; 9 \; 3] \; 2 \; 4~

~2 \; [9 \; 3 \; 2] \; 4~

~2 \; 9 \; [3 \; 2 \; 4]~

Each window has a sum of at least ~7~. A window size any smaller, such as a size ~2~, would not.

Sample Input 2

8 5
2 0 3 2 2 0 1 4

Output for Sample Input 2

4

Sample Input 3

6 3
3 3 3 3 3 3

Output for Sample Input 3

1