Score : 1000 points
There are N non-negative integers written on a blackboard. The i-th integer is A_i.
Takahashi can perform the following two kinds of operations any number of times in any order:
How many different integers not exceeding X can be written on the blackboard? We will also count the integers that are initially written on the board. Since the answer can be extremely large, find the count modulo 998244353.
Input is given from Standard Input in the following format:
N X A_1 : A_N
Print the number of different integers not exceeding X that can be written on the blackboard.
3 111 1111 10111 10010
4
Initially, 15, 23 and 18 are written on the blackboard. Among the integers not exceeding 7, four integers, 0, 3, 5 and 6, can be written. For example, 6 can be written as follows:
4 100100 1011 1110 110101 1010110
37
4 111001100101001 10111110 1001000110 100000101 11110000011
1843
1 111111111111111111111111111111111111111111111111111111111111111 1
466025955
Be sure to find the count modulo 998244353.