CF1408I.Bitwise Magic
普及/提高-
通过率:0%
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题目描述
You are given a positive integer k and an array a1,a2,…,an of non-negative distinct integers not smaller than k and not greater than 2c−1 .
In each of the next k seconds, one element is chosen randomly equiprobably out of all n elements and decreased by 1 .
For each integer x , 0≤x≤2c−1 , you need to find the probability that in the end the bitwise XOR of all elements of the array is equal to x .
Each of these values can be represented as an irreducible fraction qp , and you need to find the value of p⋅q−1 modulo 998244353 .
输入格式
The first line of input contains three integers n,k,c ( 1≤n≤(2c−k) , 1≤k≤16 , 1≤c≤16 ).
The second line contains n distinct integers a1,a2,…,an ( k≤ai≤2c−1 ).
输出格式
Print 2c integers: the probability that the bitwise XOR is equal to x in the end for x in {0,1,…,2c−1} modulo 998244353 .
输入输出样例
输入#1
4 1 3 1 2 3 4
输出#1
0 0 0 748683265 0 499122177 0 748683265