2024牛客多校：A.Bit Common

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题目描述

Given two integers nnn and mmm, among all the sequences containing nnn non-negative integers less than 2m2^m2m, you need to count the number of such sequences AAA that there exists a non-empty subsequence of AAA in which the bitwise AND of the integers is 111.

Note that a non-empty subsequence of a sequence AAA is a non-empty sequence that can be obtained by deleting zero or more elements from AAA and arranging the remaining elements in their original order.

Since the answer may be very large, output it modulo a positive integer qqq.

The bitwise AND of non-negative integers AAA and BBB, A AND BA\ \texttt{AND}\ BA AND B is defined as follows:

• When A AND BA\ \texttt{AND}\ BA AND B is written in base two, the digit in the 2d2^d2d's place (d≥0d \ge 0d