{"raw_statement":[{"iden":"problem statement","content":"Iroha is into a game where you keep pets.\nIroha's pet is Takahashi. Initially, Takahashi's **STR** and **EXP** are $X$ and $0$, respectively. These parameters increase in the following two kinds of training:\n\n*   Go to Kakomon Gym: the STR gets multiplied by $A$, and the EXP increases by $1$.\n*   Go to AtCoder Gym: the STR increases by $B$, and the EXP increases by $1$.\n\nTakahashi evolves when his STR becomes $Y$ or greater, but Iroha thinks that makes him less cute.\nFind the maximum possible EXP of Takahashi when he is trained without letting him evolve."},{"iden":"constraints","content":"*   $1 \\leq X < Y \\leq 10^{18}$\n*   $2 \\leq A \\leq 10^9$\n*   $1 \\leq B \\leq 10^9$\n*   All values in input are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$X$ $Y$ $A$ $B$"},{"iden":"sample input 1","content":"4 20 2 10"},{"iden":"sample output 1","content":"2\n\nInitially, Takahashi's STR is $4$. We can make his EXP $2$ in the following course of training:\n\n*   First, go to Kakomon Gym, which makes his STR $8$ and his EXP $1$.\n*   Then, go to AtCoder Gym, which makes his STR $18$ and his EXP $2$.\n\nOn the other hand, there is no way to train him so that his EXP becomes greater than $2$."},{"iden":"sample input 2","content":"1 1000000000000000000 10 1000000000"},{"iden":"sample output 2","content":"1000000007\n\nWatch out for overflows."}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}