{"raw_statement":[{"iden":"problem statement","content":"Given are an integer $N$ and a monotonically increasing sequence of $K$ integers $A=(A_1,A_2,\\cdots,A_K)$. Find the **lexicographically smallest** permutation $P$ of $(1,2,\\cdots,N)$ that satisfies the following condition.\n\n*   $A$ is a longest increasing subsequence of $P$ (a monotonically increasing subsequence of $P$ with the maximum possible length). It is fine if $P$ has multiple longest increasing subsequences, one of which is $A$.\n\nFrom the Constraints of this problem, we can prove that there always exists a $P$ that satisfies the condition."},{"iden":"constraints","content":"*   $1 \\leq K \\leq N \\leq 2 \\times 10^5$\n*   $1 \\leq A_1 < A_2 < \\cdots < A_K \\leq N$\n*   All values in input are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $K$\n$A_1$ $A_2$ $\\cdots$ $A_K$"},{"iden":"sample input 1","content":"3 2\n2 3"},{"iden":"sample output 1","content":"2 1 3\n\n$A$ is a longest increasing subsequence of $P$ when $P=(2,1,3),(2,3,1)$. The answer is the lexicographically smallest of the two, or $(2,1,3)$."},{"iden":"sample input 2","content":"5 1\n4"},{"iden":"sample output 2","content":"5 4 3 2 1"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}