{"raw_statement":[{"iden":"problem statement","content":"For a finite multiset $S$ of non-negative integers, let us define $\\mathrm{mex}(S)$ as the smallest non-negative integer not in $S$. For instance, $\\mathrm{mex}(\\lbrace 0,0, 1,3\\rbrace ) = 2, \\mathrm{mex}(\\lbrace 1 \\rbrace) = 0, \\mathrm{mex}(\\lbrace \\rbrace) = 0$.\nThere are $N$ non-negative integers on a blackboard. The $i$\\-th integer is $A_i$.\nYou will perform the following operation exactly $K$ times.\n\n*   Choose zero or more integers on the blackboard. Let $S$ be the multiset of chosen integers, and write $\\mathrm{mex}(S)$ on the blackboard once.\n\nHow many multisets can be the multiset of integers on the final blackboard? Find this count modulo $998244353$."},{"iden":"constraints","content":"*   $1 \\leq N,K \\leq 2\\times 10^5$\n*   $0\\leq A_i\\leq 2\\times 10^5$\n*   All numbers in the input are integers."},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$N$ $K$\n$A_1$ $A_2$ $\\ldots$ $A_N$"},{"iden":"sample input 1","content":"3 1\n0 1 3"},{"iden":"sample output 1","content":"3\n\nThe following three multisets can be obtained by the operations.\n\n*   $\\lbrace 0,0,1,3 \\rbrace$\n*   $\\lbrace 0,1,1,3\\rbrace$\n*   $\\lbrace 0,1,2,3 \\rbrace$\n\nFor instance, you can get $\\lbrace 0,1,1,3\\rbrace$ by choosing the $0$ on the blackboard to let $S=\\lbrace 0\\rbrace$ in the operation."},{"iden":"sample input 2","content":"2 1\n0 0"},{"iden":"sample output 2","content":"2\n\nThe following two multisets can be obtained by the operations.\n\n*   $\\lbrace 0,0,0 \\rbrace$\n*   $\\lbrace 0,0,1\\rbrace$\n\nNote that you may choose zero integers in the operation."},{"iden":"sample input 3","content":"5 10\n3 1 4 1 5"},{"iden":"sample output 3","content":"7109"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}