You are given an integer sequence A1,A2,…,AN of length N and an integer X.
Consider the subsequences of consecutive elements Ai,Ai+1,…,Aj (1≤i≤j≤N) whose elements sum to X or more. Write a program that finds the length of the shortest such subsequence. A subsequence holds at least one element.
The first line contains the number of test cases T.
The first line of each test case contains N (1≤N≤500,000) and X (−109≤X≤109). The second line contains the N elements of the sequence, separated by spaces. Each element is an integer between −109 and 109.
For each test case, print on one line the shortest length among the subsequences of consecutive elements whose sum is X or more. If there is no such subsequence, print −1.