B"Qwerty the Ranger took up a government job and arrived on planet Mars. He should stay in the secret lab and conduct some experiments on bacteria that have funny and abnormal properties. The job isn't difficult, but the salary is high. At the beginning of the first experiment there is a single bacterium in the test tube. Every second each bacterium in the test tube divides itself into k bacteria. After that some abnormal effects create b more bacteria in the test tube. Thus, if at the beginning of some second the test tube had x bacteria, then at the end of the second it will have kx xe2 x80 x89+ xe2 x80 x89b bacteria. The experiment showed that after n seconds there were exactly z bacteria and the experiment ended at this point. For the second experiment Qwerty is going to sterilize the test tube and put there t bacteria. He hasn't started the experiment yet but he already wonders, how many seconds he will need to grow at least z bacteria. The ranger thinks that the bacteria will divide by the same rule as in the first experiment. Help Qwerty and find the minimum number of seconds needed to get a tube with at least z bacteria in the second experiment. The first line contains four space-separated integers k, b, n and t (1 xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89k, xe2 x80 x89b, xe2 x80 x89n, xe2 x80 x89t xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89106) -- the parameters of bacterial growth, the time Qwerty needed to grow z bacteria in the first experiment and the initial number of bacteria in the second experiment, correspondingly. Print a single number -- the minimum number of seconds Qwerty needs to grow at least z bacteria in the tube."...