{"problem":{"name":"Binary Strings","description":{"content":"Snuke has written on a blackboard every integer from $1$ through $(2^N-1)$, in binary. Find the $X$\\-th lexicographically smallest string when seeing the integers on the blackboard as strings. Here, t","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"arc127_c"},"statements":[{"statement_type":"Markdown","content":"Snuke has written on a blackboard every integer from $1$ through $(2^N-1)$, in binary.\nFind the $X$\\-th lexicographically smallest string when seeing the integers on the blackboard as strings.\nHere, the input gives $N$ in decimal, but $X$ in binary.\n\n## Constraints\n\n*   $1 \\leq N \\leq 10^6$\n*   $1 \\leq X \\leq 2^N-1$\n*   $X$ is in binary.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$\n$X$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"arc127_c","tags":[],"sample_group":[["3\n101","11\n\nThe strings written on the blackboard in lexicographical order are `1`, `10`, `100`, `101`, `11`, `110`, `111`. Additionally, we have $X=101(\\mathrm{binary})=5(\\mathrm{decimal})$. Thus, the answer is `11`."],["10\n10100011","1001001111"],["1000000\n11111","1000000000000000000000000000000"]],"created_at":"2026-03-03 11:01:14"}}