A blob of mass ~N~ has discovered it has the ability to separate itself into ~P~ parts an infinite number of times. However, the blob does not split into ~P~ equal parts, but rather every ~i^{th}~ part will contain ~p_i~% of the blob's mass. Each split creates more blobs which also split, meaning the number of blobs multiplies every split. If the original blob of mass ~N~ splits into ~P~ parts ~M~ times, what is the mass of the ~k^{th}~ smallest blob?

Note that if the masses of the final blobs were {1, 1, 2, 3} the mass of the ~2^{nd}~ smallest blob would be 1.

Input Specifications

The first and line of input contains four space separated integers ~N~, ~M~, ~P~ and ~k~. The restrictions on these integers are as follows:

• ~1 \le N \le 10^9~
• ~1 \le M \le 9~
• ~2 \le P \le 5~
• k will not exceed the number of distinct blobs.

The second and last line of input will contain ~P~ integers, ~p_i~. It is guaranteed the sum of all ~p_i~ will be ~100~.

Output Specifications

A single number representing the mass of the ~k^{th}~ smallest blob. This value may be a decimal.

Sample Input

100 2 2 1
40 60

Sample Output

16