Josh does not like research. He models the ~n~ FIT2083 classes of the semester as an array, where ~a_i~ is the number of Depression Points he gains from attending the ~i~th class.

If the total number of Depression Points from a consecutive block of classes becomes strictly greater than ~k~, Josh will die. Determine the smallest number of consecutive classes he can attend and die as a result. If no such block exists, output -1.

Input

The first line contains two integers ~n~ and ~k~.

The second line contains ~n~ positive integers ~a_1, a_2, \dots, a_n~.

Output

Print a single integer: the minimum length of a contiguous subarray whose sum is strictly greater than ~k~. If no such subarray exists, print -1.

Constraints

• ~1 \le n \le 10^5~
• ~1 \le a_i \le 10^3~
• ~1 \le k \le 10^9~

Example 1

Input

5 11
5 10 1 4 5

Output

2

Explanation

The shortest valid subarray is ~[5, 10]~, whose sum is ~15 > 11~.