Earth currently has ~T~ trees. We estimate that, without human interference, this value increases by ~P \%~ each year (rounding down). However, we require wood as a natural resource, so we must cut down ~N~ trees each year.

Assume the number of trees increases by ~P \%~ before humans cut them down for the year. Determine the maximum value of ~N~ such that after ~K~ years, there are at least ~X~ trees remaining on Earth.

Constraints

~1 \le T \le 10^{14}~

~0 \le P \le 100~

~1 \le K \le 10^6~

The integer ~X~ will be given such that there is guaranteed a non-negative answer for ~N~.

Input Specification

The first and only line will contain ~4~ space-separated integers ~T~, ~P~, ~K~, and ~X~.

Output Specification

Output the maximum value of ~N~ such that after ~K~ years, there are at least ~X~ trees remaining on Earth.

Sample Input 1

100 90 3 1

Sample Output 1

105

Explanation for Sample Output 1

After 1 year: the number of trees increases from ~100~ to ~100 \times (1 + 90 \%) = 190~. We cut down ~105~ trees, leaving us with ~85~.

After 2 years: the number of trees increases from ~85~ to ~\lfloor 85 \times (1 + 90 \%) \rfloor = 161~. We cut down ~105~ trees, leaving us with ~56~.

After 3 years: the number of trees increases from ~56~ to ~\lfloor 56 \times (1 + 90 \%) \rfloor = 106~. We cut down ~105~ trees, leaving us with ~1~.

Because we have ~1~ tree remaining after ~3~ years, ~105~ is the maximum value for ~N~.

Sample Input 2

100000000000000 100 15 3000000000

Sample Output 2

100003051759392

Explanation for Sample Output 2

Make sure to use ~64~-bit integers for this problem.