CF1329B Dreamoon Likes Sequences

Dreamoon likes sequences very much. So he created a problem about the sequence that you can't find in OEIS: You are given two integers $ d, m $ , find the number of arrays $ a $ , satisfying the following constraints: - The length of $ a $ is $ n $ , $ n \ge 1 $ - $ 1 \le a_1 < a_2 < \dots < a_n \le d $ - Define an array $ b $ of length $ n $ as follows: $ b_1 = a_1 $ , $ \forall i > 1, b_i = b_{i - 1} \oplus a_i $ , where $ \oplus $ is the bitwise exclusive-or (xor). After constructing an array $ b $ , the constraint $ b_1 < b_2 < \dots < b_{n - 1} < b_n $ should hold. Since the number of possible arrays may be too large, you need to find the answer modulo $ m $ .

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