AT_abc423_f [ABC423F] Loud Cicada

AtCoder Island has $ N $ species of cicadas. Cicadas of species $ i $ ( $ 1 \leq i \leq N $ ) have mass outbreaks only in years that are multiples of $ A_i $ . Among the $ Y $ years from year $ 1 $ to year $ Y $ , find how many years have mass outbreaks of exactly $ M $ species of cicadas.

The input is given from Standard Input in the following format: > $ N $ $ M $ $ Y $ $ A_1 $ $ \cdots $ $ A_N $

Output the answer.

### Sample Explanation 1 From years $ 1 $ to $ 16 $ , each species of cicada has mass outbreaks in the following years: - Species $ 1 $ cicadas have mass outbreaks in years $ 4,8,12,16 $ . - Species $ 2 $ cicadas have mass outbreaks in years $ 2,4,6,8,10,12,14,16 $ . - Species $ 3 $ cicadas have mass outbreaks in years $ 3,6,9,12,15 $ . From years $ 1 $ to $ 16 $ , exactly two species of cicadas have mass outbreaks four times in years $ 4,6,8,16 $ . ### Sample Explanation 2 The answer may not fit in a 32-bit integer. ### Sample Explanation 3 Input values may not fit in a 32-bit integer. ### Constraints - $ 1 \leq M \leq N \leq 20 $ - $ 1 \leq Y \leq 10^{18} $ - $ 1 \leq A_i \leq 10^{18} $ ( $ 1 \leq i \leq N $ ) - All input values are integers.