Count Disjoint Arrays

Given an integer $M$, count the number of non-empty arrays $A$ satisfying the following conditions - $1 \le A_i \le M$ for all $1 \le i \le |A|$ - $A_i$ $\&$ $A_j = 0$ for all $1 \le i < j \le |A|$, where $\&$ denotes Bitwise AND operator. Since the answer may be large, find it modulo $998244353$. ### Input - The first line of input will contain a single integer $T$, denoting the number of test