{"problem":{"name":"Buy an Integer","description":{"content":"Takahashi has come to an integer shop to buy an integer. The shop sells the integers from $1$ through $10^9$. The integer $N$ is sold for $A \\times N + B \\times d(N)$ yen (the currency of Japan), wher","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc146_c"},"statements":[{"statement_type":"Markdown","content":"Takahashi has come to an integer shop to buy an integer.\nThe shop sells the integers from $1$ through $10^9$. The integer $N$ is sold for $A \\times N + B \\times d(N)$ yen (the currency of Japan), where $d(N)$ is the number of digits in the decimal notation of $N$.\nFind the largest integer that Takahashi can buy when he has $X$ yen. If no integer can be bought, print $0$.\n\n## Constraints\n\n*   All values in input are integers.\n*   $1 \\leq A \\leq 10^9$\n*   $1 \\leq B \\leq 10^9$\n*   $1 \\leq X \\leq 10^{18}$\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$A$ $B$ $X$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc146_c","tags":[],"sample_group":[["10 7 100","9\n\nThe integer $9$ is sold for $10 \\times 9 + 7 \\times 1 = 97$ yen, and this is the greatest integer that can be bought. Some of the other integers are sold for the following prices:\n\n*   $10: 10 \\times 10 + 7 \\times 2 = 114$ yen\n*   $100: 10 \\times 100 + 7 \\times 3 = 1021$ yen\n*   $12345: 10 \\times 12345 + 7 \\times 5 = 123485$ yen"],["2 1 100000000000","1000000000\n\nHe can buy the largest integer that is sold. Note that input may not fit into a $32$\\-bit integer type."],["1000000000 1000000000 100","0"],["1234 56789 314159265","254309"]],"created_at":"2026-03-03 11:01:14"}}