Interesting Sequence

Consider a sequence of length 2K, where K is a positive integer. If both the sum of the first K elements and the sum of the last K elements are at most S, call the sequence interesting.

Given a sequence A of length N, find, for every starting position, the maximum length of a contiguous subsequence that starts there and is interesting.

The first line contains N and S. (2 <= N <= 100,000, 1 <= S <= 2 * 10^9)

Each of the next N lines contains one element of the sequence A. Every element is positive, and the sum of all elements of A is at most 2 * 10^9.

Print N lines. On the i-th line, print the length of the longest interesting contiguous subsequence that starts at the i-th element. If no such subsequence exists, print 0.