18466번 - Ignore Submasks 다국어

문제

You are given an array of n integers, a₁, a₂, . . . , a_n. Each integer is between 0 and 2^k − 1, inclusive.

Let’s say that f(x) is the smallest i, such that (a_i&x) ≠ a_i, or 0, if there are no such i. (a&b) is the bitwise AND operation.

Find f(0) + f(1) + . . . + f(2^k − 1). As this value may be very large, find it modulo 998 244 353.

입력

The first line contains two integers: n, k (1 ≤ n ≤ 100, 1 ≤ k ≤ 60).

The next line contains n integers: a₁, a₂, . . . , a_n (0 ≤ a_i < 2^k).

출력

Print one integer: f(0) + f(1) + . . . + f(2^k − 1), modulo 998 244 353.

제한

힌트

In the first example, f(0) = 2, f(1) = 0.

In the second example, f(0) = 1, f(1) = 1, f(2) = 2, f(3) = 0.