Given an array ~a~ of ~N~ integers, find the shortest length subarray that has a sum greater than or equal to ~M~.

Input Specification

The first line will contain ~2~ integers, ~N, M~ ~(1 \le N \le 10^5, 1 \le M \le 10^9)~.

The second line will contain ~N~ integers ~a_1, a_2, \ldots, a_N~ ~(|a_i| \le 10^7)~.

Output Specification

Output the shortest length subarray that has a sum greater than or equal to ~M~. If there is no subarray, print -1.

Sample Input

6 3
2 0 -1 2 -1 2

Sample Output

3