Given positive integers , a_1, a_2, , a_N, you are required to compute \mathrm{floor}(\log_b a_1), , \mathrm{floor}(\log_b a_N), where denotes the greatest integer not exceeding .
The input file contains the numbers , , a_1, a_2, , a_N in a single line.
The output file should contain integers—the results of the calculations.
1 \leq N \leq 1000, 2 \leq b \leq 100, 1 \leq a_i < 10^{1000} (i.e., each number may contain up to digits).
Example 1