You are given an integer array a of length n and an integer x.

In one operation, you can remove the leftmost or rightmost element from the array. The value of the removed element is then subtracted from $x$.

Your goal is to perform a minimum number of such operations so that $x$ becomes exactly $0$. If it's not possible, print $-1$.

Note: The removed elements no longer appear in the array for future operations.

The first line contains two integers $n$ and $x$ ($1 \le n \le 10^5$, $1 \le x \le 10^9$) --- the size of the array and the target value.

The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \le a_i \le 10^4$) --- the elements of the array.

Print a single integer --- the minimum number of operations to make $x$ exactly zero, or $-1$ if it is not possible.