Suffering

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

5 11
5 10 1 4 5

2

Explanation

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