This is the hard version of the problem. The only difference between easy and hard versions is the constraint of m . You can make hacks only if both versions are solved. Chiori loves dolls and now she is going to decorate her bedroom! As a doll collector, Chiori has got n dolls. The i -th doll has a non-negative integer value a_i ( a_i < 2^m , m is given). Chiori wants to pick some (maybe zero) dolls for the decoration, so there are 2^n different picking ways. Let x be the bitwise-xor-sum of values of dolls Chiori picks (in case Chiori picks no dolls x = 0 ). The value of this picking way is equal to the number of 1 -bits in the binary representation of x . More formally, it is also equal to the number of indices 0 <= q i < m , such that <= ft lfloor frac{x}{2^i} right rfloor is odd. Tell her the number of picking ways with value i for each integer i from 0 to m . Due to the answers can be very huge, print them by modulo 998 ,244 ,353 . The first line contains two integers n and m ( 1 <= n <= 2 cdot 10^5 , 0 <= m <= 53 ) -- the number of dolls and the maximum value of the picking way. The second line contains n integers a_1, a_2, ldots, a_n ( 0 <= a_i < 2^m ) -- the values of dolls. Print m+1 integers p_0, p_1, ldots, p_m -- p_i is equal to the number of picking ways with value i by modulo 998 ,244 ,353 .