There is a complete binary tree which includes n nodes. Each node on the tree has a weight w, each edge on the tree is directed from the parent node to the child node. Give you a pen, draw from the any node along the directed edge at one stroke. It is required that the sum of those drawn nodes’ s weight is no more than k. How many node can be drawn at most in one stroke?

The first line input an positive integer T(1<=T<=10)indicates the number of test cases. Next, each case occupies two lines. The first line input two positive integers n(1<=n<=10^6) and k,(1<=k<=10^9)

The second line input n integers w(1<=w <=10^3),, indicate the weight of nodes from the first level of the tree and from left to right.

For each test cases, output one line with the most number of nodes can be drawn in one stroke. If any node likes this doesn’t exists, output -1.