{"raw_statement":[{"iden":"problem statement","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."},{"iden":"constraints","content":"*   $1 \\leq N \\leq 10^6$\n*   $1 \\leq X \\leq 2^N-1$\n*   $X$ is in binary."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$\n$X$"},{"iden":"sample input 1","content":"3\n101"},{"iden":"sample output 1","content":"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`."},{"iden":"sample input 2","content":"10\n10100011"},{"iden":"sample output 2","content":"1001001111"},{"iden":"sample input 3","content":"1000000\n11111"},{"iden":"sample output 3","content":"1000000000000000000000000000000"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}